Inference and foundations

Filter results by

Search Help
Currently selected filters that can be removed

Keyword(s)

Geography

1 facets displayed. 0 facets selected.

Survey or statistical program

2 facets displayed. 0 facets selected.

Content

1 facets displayed. 0 facets selected.
Sort Help
entries

Results

All (100)

All (100) (10 to 20 of 100 results)

  • Articles and reports: 12-001-X202200200008
    Description:

    This response contains additional remarks on a few selected issues raised by the discussants.

    Release date: 2022-12-15

  • Articles and reports: 12-001-X202200200011
    Description:

    Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.

    Release date: 2022-12-15

  • Articles and reports: 12-001-X202200100004
    Description:

    When the sample size of an area is small, borrowing information from neighbors is a small area estimation technique to provide more reliable estimates. One of the famous models in small area estimation is a multinomial-Dirichlet hierarchical model for multinomial counts. Due to natural characteristics of the data, making unimodal order restriction assumption to parameter spaces is relevant. In our application, body mass index is more likely at an overweight level, which means the unimodal order restriction may be reasonable. The same unimodal order restriction for all areas may be too strong to be true for some cases. To increase flexibility, we add uncertainty to the unimodal order restriction. Each area will have similar unimodal patterns, but not the same. Since the order restriction with uncertainty increases the inference difficulty, we make comparison with the posterior summaries and approximated log-pseudo marginal likelihood.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202200100009
    Description:

    In finite population estimation, the inverse probability or Horvitz-Thompson estimator is a basic tool. Even when auxiliary information is available to model the variable of interest, it is still used to estimate the model error. Here, the inverse probability estimator is generalized by introducing a positive definite matrix. The usual inverse probability estimator is a special case of the generalized estimator, where the positive definite matrix is the identity matrix. Since calibration estimation seeks weights that are close to the inverse probability weights, it too can be generalized by seeking weights that are close to those of the generalized inverse probability estimator. Calibration is known to be optimal, in the sense that it asymptotically attains the Godambe-Joshi lower bound. That lower bound has been derived under a model where no correlation is present. This too, can be generalized to allow for correlation. With the correct choice of the positive definite matrix that generalizes the calibration estimators, this generalized lower bound can be asymptotically attained. There is often no closed-form formula for the generalized estimators. However, simple explicit examples are given here to illustrate how the generalized estimators take advantage of the correlation. This simplicity is achieved here, by assuming a correlation of one between some population units. Those simple estimators can still be useful, even if the correlation is smaller than one. Simulation results are used to compare the generalized estimators to the ordinary estimators.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100200003
    Description:

    Calibration weighting is a statistically efficient way for handling unit nonresponse. Assuming the response (or output) model justifying the calibration-weight adjustment is correct, it is often possible to measure the variance of estimates in an asymptotically unbiased manner. One approach to variance estimation is to create jackknife replicate weights. Sometimes, however, the conventional method for computing jackknife replicate weights for calibrated analysis weights fails. In that case, an alternative method for computing jackknife replicate weights is usually available. That method is described here and then applied to a simple example.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X202100200006
    Description:

    Sample-based calibration occurs when the weights of a survey are calibrated to control totals that are random, instead of representing fixed population-level totals. Control totals may be estimated from different phases of the same survey or from another survey. Under sample-based calibration, valid variance estimation requires that the error contribution due to estimating the control totals be accounted for. We propose a new variance estimation method that directly uses the replicate weights from two surveys, one survey being used to provide control totals for calibration of the other survey weights. No restrictions are set on the nature of the two replication methods and no variance-covariance estimates need to be computed, making the proposed method straightforward to implement in practice. A general description of the method for surveys with two arbitrary replication methods with different numbers of replicates is provided. It is shown that the resulting variance estimator is consistent for the asymptotic variance of the calibrated estimator, when calibration is done using regression estimation or raking. The method is illustrated in a real-world application, in which the demographic composition of two surveys needs to be harmonized to improve the comparability of the survey estimates.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X202000100001
    Description:

    For several decades, national statistical agencies around the world have been using probability surveys as their preferred tool to meet information needs about a population of interest. In the last few years, there has been a wind of change and other data sources are being increasingly explored. Five key factors are behind this trend: the decline in response rates in probability surveys, the high cost of data collection, the increased burden on respondents, the desire for access to “real-time” statistics, and the proliferation of non-probability data sources. Some people have even come to believe that probability surveys could gradually disappear. In this article, we review some approaches that can reduce, or even eliminate, the use of probability surveys, all the while preserving a valid statistical inference framework. All the approaches we consider use data from a non-probability source; data from a probability survey are also used in most cases. Some of these approaches rely on the validity of model assumptions, which contrasts with approaches based on the probability sampling design. These design-based approaches are generally not as efficient; yet, they are not subject to the risk of bias due to model misspecification.

    Release date: 2020-06-30

  • Articles and reports: 12-001-X201800254956
    Description:

    In Italy, the Labor Force Survey (LFS) is conducted quarterly by the National Statistical Institute (ISTAT) to produce estimates of the labor force status of the population at different geographical levels. In particular, ISTAT provides LFS estimates of employed and unemployed counts for local Labor Market Areas (LMAs). LMAs are 611 sub-regional clusters of municipalities and are unplanned domains for which direct estimates have overly large sampling errors. This implies the need of Small Area Estimation (SAE) methods. In this paper, we develop a new area level SAE method that uses a Latent Markov Model (LMM) as linking model. In LMMs, the characteristic of interest, and its evolution in time, is represented by a latent process that follows a Markov chain, usually of first order. Therefore, areas are allowed to change their latent state across time. The proposed model is applied to quarterly data from the LFS for the period 2004 to 2014 and fitted within a hierarchical Bayesian framework using a data augmentation Gibbs sampler. Estimates are compared with those obtained by the classical Fay-Herriot model, by a time-series area level SAE model, and on the basis of data coming from the 2011 Population Census.

    Release date: 2018-12-20

  • Articles and reports: 12-001-X201800154928
    Description:

    A two-phase process was used by the Substance Abuse and Mental Health Services Administration to estimate the proportion of US adults with serious mental illness (SMI). The first phase was the annual National Survey on Drug Use and Health (NSDUH), while the second phase was a random subsample of adult respondents to the NSDUH. Respondents to the second phase of sampling were clinically evaluated for serious mental illness. A logistic prediction model was fit to this subsample with the SMI status (yes or no) determined by the second-phase instrument treated as the dependent variable and related variables collected on the NSDUH from all adults as the model’s explanatory variables. Estimates were then computed for SMI prevalence among all adults and within adult subpopulations by assigning an SMI status to each NSDUH respondent based on comparing his (her) estimated probability of having SMI to a chosen cut point on the distribution of the predicted probabilities. We investigate alternatives to this standard cut point estimator such as the probability estimator. The latter assigns an estimated probability of having SMI to each NSDUH respondent. The estimated prevalence of SMI is the weighted mean of those estimated probabilities. Using data from NSDUH and its subsample, we show that, although the probability estimator has a smaller mean squared error when estimating SMI prevalence among all adults, it has a greater tendency to be biased at the subpopulation level than the standard cut point estimator.

    Release date: 2018-06-21

  • Articles and reports: 12-001-X201700254872
    Description:

    This note discusses the theoretical foundations for the extension of the Wilson two-sided coverage interval to an estimated proportion computed from complex survey data. The interval is shown to be asymptotically equivalent to an interval derived from a logistic transformation. A mildly better version is discussed, but users may prefer constructing a one-sided interval already in the literature.

    Release date: 2017-12-21
Data (0)

Data (0) (0 results)

No content available at this time.

Analysis (92)

Analysis (92) (10 to 20 of 92 results)

  • Articles and reports: 12-001-X202200200008
    Description:

    This response contains additional remarks on a few selected issues raised by the discussants.

    Release date: 2022-12-15

  • Articles and reports: 12-001-X202200200011
    Description:

    Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.

    Release date: 2022-12-15

  • Articles and reports: 12-001-X202200100004
    Description:

    When the sample size of an area is small, borrowing information from neighbors is a small area estimation technique to provide more reliable estimates. One of the famous models in small area estimation is a multinomial-Dirichlet hierarchical model for multinomial counts. Due to natural characteristics of the data, making unimodal order restriction assumption to parameter spaces is relevant. In our application, body mass index is more likely at an overweight level, which means the unimodal order restriction may be reasonable. The same unimodal order restriction for all areas may be too strong to be true for some cases. To increase flexibility, we add uncertainty to the unimodal order restriction. Each area will have similar unimodal patterns, but not the same. Since the order restriction with uncertainty increases the inference difficulty, we make comparison with the posterior summaries and approximated log-pseudo marginal likelihood.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202200100009
    Description:

    In finite population estimation, the inverse probability or Horvitz-Thompson estimator is a basic tool. Even when auxiliary information is available to model the variable of interest, it is still used to estimate the model error. Here, the inverse probability estimator is generalized by introducing a positive definite matrix. The usual inverse probability estimator is a special case of the generalized estimator, where the positive definite matrix is the identity matrix. Since calibration estimation seeks weights that are close to the inverse probability weights, it too can be generalized by seeking weights that are close to those of the generalized inverse probability estimator. Calibration is known to be optimal, in the sense that it asymptotically attains the Godambe-Joshi lower bound. That lower bound has been derived under a model where no correlation is present. This too, can be generalized to allow for correlation. With the correct choice of the positive definite matrix that generalizes the calibration estimators, this generalized lower bound can be asymptotically attained. There is often no closed-form formula for the generalized estimators. However, simple explicit examples are given here to illustrate how the generalized estimators take advantage of the correlation. This simplicity is achieved here, by assuming a correlation of one between some population units. Those simple estimators can still be useful, even if the correlation is smaller than one. Simulation results are used to compare the generalized estimators to the ordinary estimators.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100200003
    Description:

    Calibration weighting is a statistically efficient way for handling unit nonresponse. Assuming the response (or output) model justifying the calibration-weight adjustment is correct, it is often possible to measure the variance of estimates in an asymptotically unbiased manner. One approach to variance estimation is to create jackknife replicate weights. Sometimes, however, the conventional method for computing jackknife replicate weights for calibrated analysis weights fails. In that case, an alternative method for computing jackknife replicate weights is usually available. That method is described here and then applied to a simple example.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X202100200006
    Description:

    Sample-based calibration occurs when the weights of a survey are calibrated to control totals that are random, instead of representing fixed population-level totals. Control totals may be estimated from different phases of the same survey or from another survey. Under sample-based calibration, valid variance estimation requires that the error contribution due to estimating the control totals be accounted for. We propose a new variance estimation method that directly uses the replicate weights from two surveys, one survey being used to provide control totals for calibration of the other survey weights. No restrictions are set on the nature of the two replication methods and no variance-covariance estimates need to be computed, making the proposed method straightforward to implement in practice. A general description of the method for surveys with two arbitrary replication methods with different numbers of replicates is provided. It is shown that the resulting variance estimator is consistent for the asymptotic variance of the calibrated estimator, when calibration is done using regression estimation or raking. The method is illustrated in a real-world application, in which the demographic composition of two surveys needs to be harmonized to improve the comparability of the survey estimates.

    Release date: 2022-01-06

  • Articles and reports: 12-001-X202000100001
    Description:

    For several decades, national statistical agencies around the world have been using probability surveys as their preferred tool to meet information needs about a population of interest. In the last few years, there has been a wind of change and other data sources are being increasingly explored. Five key factors are behind this trend: the decline in response rates in probability surveys, the high cost of data collection, the increased burden on respondents, the desire for access to “real-time” statistics, and the proliferation of non-probability data sources. Some people have even come to believe that probability surveys could gradually disappear. In this article, we review some approaches that can reduce, or even eliminate, the use of probability surveys, all the while preserving a valid statistical inference framework. All the approaches we consider use data from a non-probability source; data from a probability survey are also used in most cases. Some of these approaches rely on the validity of model assumptions, which contrasts with approaches based on the probability sampling design. These design-based approaches are generally not as efficient; yet, they are not subject to the risk of bias due to model misspecification.

    Release date: 2020-06-30

  • Articles and reports: 12-001-X201800254956
    Description:

    In Italy, the Labor Force Survey (LFS) is conducted quarterly by the National Statistical Institute (ISTAT) to produce estimates of the labor force status of the population at different geographical levels. In particular, ISTAT provides LFS estimates of employed and unemployed counts for local Labor Market Areas (LMAs). LMAs are 611 sub-regional clusters of municipalities and are unplanned domains for which direct estimates have overly large sampling errors. This implies the need of Small Area Estimation (SAE) methods. In this paper, we develop a new area level SAE method that uses a Latent Markov Model (LMM) as linking model. In LMMs, the characteristic of interest, and its evolution in time, is represented by a latent process that follows a Markov chain, usually of first order. Therefore, areas are allowed to change their latent state across time. The proposed model is applied to quarterly data from the LFS for the period 2004 to 2014 and fitted within a hierarchical Bayesian framework using a data augmentation Gibbs sampler. Estimates are compared with those obtained by the classical Fay-Herriot model, by a time-series area level SAE model, and on the basis of data coming from the 2011 Population Census.

    Release date: 2018-12-20

  • Articles and reports: 12-001-X201800154928
    Description:

    A two-phase process was used by the Substance Abuse and Mental Health Services Administration to estimate the proportion of US adults with serious mental illness (SMI). The first phase was the annual National Survey on Drug Use and Health (NSDUH), while the second phase was a random subsample of adult respondents to the NSDUH. Respondents to the second phase of sampling were clinically evaluated for serious mental illness. A logistic prediction model was fit to this subsample with the SMI status (yes or no) determined by the second-phase instrument treated as the dependent variable and related variables collected on the NSDUH from all adults as the model’s explanatory variables. Estimates were then computed for SMI prevalence among all adults and within adult subpopulations by assigning an SMI status to each NSDUH respondent based on comparing his (her) estimated probability of having SMI to a chosen cut point on the distribution of the predicted probabilities. We investigate alternatives to this standard cut point estimator such as the probability estimator. The latter assigns an estimated probability of having SMI to each NSDUH respondent. The estimated prevalence of SMI is the weighted mean of those estimated probabilities. Using data from NSDUH and its subsample, we show that, although the probability estimator has a smaller mean squared error when estimating SMI prevalence among all adults, it has a greater tendency to be biased at the subpopulation level than the standard cut point estimator.

    Release date: 2018-06-21

  • Articles and reports: 12-001-X201700254872
    Description:

    This note discusses the theoretical foundations for the extension of the Wilson two-sided coverage interval to an estimated proportion computed from complex survey data. The interval is shown to be asymptotically equivalent to an interval derived from a logistic transformation. A mildly better version is discussed, but users may prefer constructing a one-sided interval already in the literature.

    Release date: 2017-12-21
Reference (8)

Reference (8) ((8 results))

  • Surveys and statistical programs – Documentation: 11-522-X201300014259
    Description:

    In an effort to reduce response burden on farm operators, Statistics Canada is studying alternative approaches to telephone surveys for producing field crop estimates. One option is to publish harvested area and yield estimates in September as is currently done, but to calculate them using models based on satellite and weather data, and data from the July telephone survey. However before adopting such an approach, a method must be found which produces estimates with a sufficient level of accuracy. Research is taking place to investigate different possibilities. Initial research results and issues to consider are discussed in this paper.

    Release date: 2014-10-31

  • Surveys and statistical programs – Documentation: 12-002-X20040027035
    Description:

    As part of the processing of the National Longitudinal Survey of Children and Youth (NLSCY) cycle 4 data, historical revisions have been made to the data of the first 3 cycles, either to correct errors or to update the data. During processing, particular attention was given to the PERSRUK (Person Identifier) and the FIELDRUK (Household Identifier). The same level of attention has not been given to the other identifiers that are included in the data base, the CHILDID (Person identifier) and the _IDHD01 (Household identifier). These identifiers have been created for the public files and can also be found in the master files by default. The PERSRUK should be used to link records between files and the FIELDRUK to determine the household when using the master files.

    Release date: 2004-10-05

  • Surveys and statistical programs – Documentation: 13F0026M2001003
    Description:

    Initial results from the Survey of Financial Security (SFS), which provides information on the net worth of Canadians, were released on March 15 2001, in The daily. The survey collected information on the value of the financial and non-financial assets owned by each family unit and on the amount of their debt.

    Statistics Canada is currently refining this initial estimate of net worth by adding to it an estimate of the value of benefits accrued in employer pension plans. This is an important addition to any asset and debt survey as, for many family units, it is likely to be one of the largest assets. With the aging of the population, information on pension accumulations is greatly needed to better understand the financial situation of those nearing retirement. These updated estimates of the Survey of Financial Security will be released in late fall 2001.

    The process for estimating the value of employer pension plan benefits is a complex one. This document describes the methodology for estimating that value, for the following groups: a) persons who belonged to an RPP at the time of the survey (referred to as current plan members); b) persons who had previously belonged to an RPP and either left the money in the plan or transferred it to a new plan; c) persons who are receiving RPP benefits.

    This methodology was proposed by Hubert Frenken and Michael Cohen. The former has many years of experience with Statistics Canada working with data on employer pension plans; the latter is a principal with the actuarial consulting firm William M. Mercer. Earlier this year, Statistics Canada carried out a public consultation on the proposed methodology. This report includes updates made as a result of feedback received from data users.

    Release date: 2001-09-05

  • Surveys and statistical programs – Documentation: 13F0026M2001002
    Description:

    The Survey of Financial Security (SFS) will provide information on the net worth of Canadians. In order to do this, information was collected - in May and June 1999 - on the value of the assets and debts of each of the families or unattached individuals in the sample. The value of one particular asset is not easy to determine, or to estimate. That is the present value of the amount people have accrued in their employer pension plan. These plans are often called registered pension plans (RPP), as they must be registered with Canada Customs and Revenue Agency. Although some RPP members receive estimates of the value of their accrued benefit, in most cases plan members would not know this amount. However, it is likely to be one of the largest assets for many family units. And, as the baby boomers approach retirement, information on their pension accumulations is much needed to better understand their financial readiness for this transition.

    The intent of this paper is to: present, for discussion, a methodology for estimating the present value of employer pension plan benefits for the Survey of Financial Security; and to seek feedback on the proposed methodology. This document proposes a methodology for estimating the value of employer pension plan benefits for the following groups:a) persons who belonged to an RPP at the time of the survey (referred to as current plan members); b) persons who had previously belonged to an RPP and either left the money in the plan or transferred it to a new plan; c) persons who are receiving RPP benefits.

    Release date: 2001-02-07

  • Surveys and statistical programs – Documentation: 11-522-X19990015642
    Description:

    The Longitudinal Immigration Database (IMDB) links immigration and taxation administrative records into a comprehensive source of data on the labour market behaviour of the landed immigrant population in Canada. It covers the period 1980 to 1995 and will be updated annually starting with the 1996 tax year in 1999. Statistics Canada manages the database on behalf of a federal-provincial consortium led by Citizenship and Immigration Canada. The IMDB was created specifically to respond to the need for detailed and reliable data on the performance and impact of immigration policies and programs. It is the only source of data at Statistics Canada that provides a direct link between immigration policy levers and the economic performance of immigrants. The paper will examine the issues related to the development of a longitudinal database combining administrative records to support policy-relevant research and analysis. Discussion will focus specifically on the methodological, conceptual, analytical and privacy issues involved in the creation and ongoing development of this database. The paper will also touch briefly on research findings, which illustrate the policy outcome links the IMDB allows policy-makers to investigate.

    Release date: 2000-03-02

  • Surveys and statistical programs – Documentation: 11-522-X19990015650
    Description:

    The U.S. Manufacturing Plant Ownership Change Database (OCD) was constructed using plant-level data taken from the Census Bureau's Longitudinal Research Database (LRD). It contains data on all manufacturing plants that have experienced ownership change at least once during the period 1963-92. This paper reports the status of the OCD and discuss its research possibilities. For an empirical demonstration, data taken from the database are used to study the effects of ownership changes on plant closure.

    Release date: 2000-03-02

  • Surveys and statistical programs – Documentation: 11-522-X19990015658
    Description:

    Radon, a naturally occurring gas found at some level in most homes, is an established risk factor for human lung cancer. The U.S. National Research Council (1999) has recently completed a comprehensive evaluation of the health risks of residential exposure to radon, and developed models for projecting radon lung cancer risks in the general population. This analysis suggests that radon may play a role in the etiology of 10-15% of all lung cancer cases in the United States, although these estimates are subject to considerable uncertainty. In this article, we present a partial analysis of uncertainty and variability in estimates of lung cancer risk due to residential exposure to radon in the United States using a general framework for the analysis of uncertainty and variability that we have developed previously. Specifically, we focus on estimates of the age-specific excess relative risk (ERR) and lifetime relative risk (LRR), both of which vary substantially among individuals.

    Release date: 2000-03-02

  • Geographic files and documentation: 92F0138M1993001
    Geography: Canada
    Description:

    The Geography Divisions of Statistics Canada and the U.S. Bureau of the Census have commenced a cooperative research program in order to foster an improved and expanded perspective on geographic areas and their relevance. One of the major objectives is to determine a common geographic area to form a geostatistical basis for cross-border research, analysis and mapping.

    This report, which represents the first stage of the research, provides a list of comparable pairs of Canadian and U.S. standard geographic areas based on current definitions. Statistics Canada and the U.S. Bureau of the Census have two basic types of standard geographic entities: legislative/administrative areas (called "legal" entities in the U.S.) and statistical areas.

    The preliminary pairing of geographic areas are based on face-value definitions only. The definitions are based on the June 4, 1991 Census of Population and Housing for Canada and the April 1, 1990 Census of Population and Housing for the U.S.A. The important aspect is the overall conceptual comparability, not the precise numerical thresholds used for delineating the areas.

    Data users should use this report as a general guide to compare the census geographic areas of Canada and the United States, and should be aware that differences in settlement patterns and population levels preclude a precise one-to-one relationship between conceptually similar areas. The geographic areas compared in this report provide a framework for further empirical research and analysis.

    Release date: 1999-03-05
Date modified: