Inference and foundations

Results

All (120)

All (120) (0 to 10 of 120 results)

1. Small area estimation of general indicators in off-census years
Articles and reports: 12-001-X202600100012
Description: We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a larger unit-level survey that adequately covers the areas of interest and contains the values of useful auxiliary variables. However, the minimal data requirement of the proposed method is a single survey with microdata on the target variable and suitable auxiliary variables for the period of interest. We also develop an estimator of the mean squared error (MSE) that accounts for the uncertainty introduced by the large survey used to replace the census of auxiliary information. Our empirical results indicate that the proposed predictors perform clearly better than the alternative predictors when census data are outdated, and are very close to optimal ones when census data are correct. They also illustrate that the proposed total MSE estimator corrects for the bias of purely model-based MSE estimators that do not account for the large survey uncertainty.
Release date: 2026-06-29
2. Improved small area inference from data integration using global-local priors
Articles and reports: 12-001-X202500200009
Description: We present and apply methodology to improve inference for small area parameters by using data from several sources. This work extends Cahoy and Sedransk (2023) who showed how to integrate summary statistics from several sources. Our methodology uses hierarchical global-local prior distributions to make inferences for the proportion of individuals in Florida’s counties who do not have health insurance. Results from an extensive simulation study show that this methodology will provide improved inference by using several data sources. Among the five model variants evaluated the ones using horseshoe priors for all variances have better performance than the ones using lasso priors for the local variances.
Release date: 2025-12-23
3. Approximate hierarchical Bayes small area estimation using Natural Exponential Family with Quadratic Variance Function and poststratification
Articles and reports: 12-001-X202500200011
Description: We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function (NEF-QVF) in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.
Release date: 2025-12-23
4. Comparison of Recent Techniques of Combining Probability and Non-probability Samples Archived
Articles and reports: 11-522-X202500100031
Description: Several recent quasi-randomization methods for inferences from non-probability samples will be compared. The considered techniques are developed under the assumption that the sample selection is governed by an underlying latent random mechanism and that it can be uncovered by combining non-probability survey data with a "reference" probability-based sample, obtained from the same target population. Challenges prompting the development of alternative procedures include (i) non-probability sample participation indicators are available only on the observed sample units and (ii) it is not generally known which units from the underlying population belong to both the non-probability and reference samples. The ways different procedures address these challenges are considered, theoretical properties of the methods are discussed and their comparison is made using simulations.
Release date: 2025-09-08
5. Propensity Score Estimation and Optimal Sampling Design when Integrating Probability Samples with Non-probability Data Archived
Articles and reports: 11-522-X202500100032
Description: Although non-probability data sources are not new to official statistics, a revived interest in the topic has emerged from pressures due to falling survey response rates, increasing data collection costs and a desire to take advantage of new data source opportunities from the ongoing societal digitalisation. Due to the exclusion of certain segments of the target population, inference derived solely from a non-probability data source is likely to result in bias. This work approaches the challenge of addressing the bias by integrating non-probability data with reference probability samples. The focus will be on methods to model the propensity of inclusion in the non-probability dataset with the help of the accompanying reference sample, with the modelled propensities then applied in an inverse probability weighting approach to produce population estimates. The reference sample is sometimes assumed as given. In this presentation however, an objective of finding an optimal strategy will be pursued that is, the combination of a data integration-based estimator and sample design for the reference probability sample. Recent work is discussed in which advantage is taken of the good unit identification possibilities in business surveys to study an estimator based on propensities and derive optimal (unequal) selection probabilities for the reference sample.
Release date: 2025-09-08
6. Mean squared prediction error estimators of the empirical best linear unbiased predictor of a small area mean under a semi-parametric Fay-Herriot model
Articles and reports: 12-001-X202500100005
Description: In this paper, we derive a second-order unbiased (or nearly unbiased) mean squared prediction error (MSPE) estimator of the empirical best linear unbiased predictor (EBLUP) of a small area mean for a semi-parametric extension to the well-known Fay-Herriot model. Specifically, we derive our MSPE estimator essentially assuming certain moment conditions on both the sampling errors and random effects distributions. The normality-based Prasad-Rao MSPE estimator has a surprising robustness property in that it remains second-order unbiased under the non-normality of random effects when a simple Prasad-Rao method-of-moments estimator is used for the variance component and the sampling error distribution is normal. We show that the normality-based MSPE estimator is no longer second-order unbiased when the sampling error distribution has non-zero kurtosis or when the Fay-Herriot moment method is used to estimate the variance component, even when the sampling error distribution is normal. Interestingly, when the simple method-of moments estimator is used for the variance component, our proposed MSPE estimator does not require the estimation of kurtosis of the random effects. Results of a simulation study on the accuracy of the proposed MSPE estimator, under non-normality of both sampling and random effects distributions, are also presented.
Release date: 2025-06-30
7. Bridging BigData and sampling methodology: What is big and where is the bridge?
Articles and reports: 12-001-X202500100009
Description: BigData users and the BigData research community are expanding rapidly, while statisticians at large are seemingly becoming divided between those who are enthusiastic and those who are concerned, if not downright hostile. Is BigData also a big step ahead, truly advancing our ability to extract meaningful information and actual knowledge from data? Is BigData underplaying traditional statistical inference as we know it, supplanting survey methodology as a low-cost futuristic option? In this paper I will attempt to unravel the multifaceted relationship bridging BigData to sampling methodology. Starting by reasoning why it should be interesting to look at BigData from a sampling statistician’s perspective, I will delve deeper into the somewhat ambiguous definition of BigData and share some very personal considerations and views on the matter. In the process, several open questions will arise while discussing a personal selection of insights that are traceable through the vast body of statistical literature around BigData and sampling methodology. The discussion will take various angles explored across nine key points, and it will conclude with a forward-looking perspective on a main challenge for future research: addressing the strong assumptions needed to manage deviations from purely randomized data collection.
Release date: 2025-06-30
8. Trends and directions in sample survey theory and methods
Articles and reports: 12-001-X202500100014
Description: Rao (1999) summarized trends in sample survey theory and methods at the turn of the millenium. We provide an updated discussion of some current trends in survey design and estimation methods for the 50th anniversary of Survey Methodology. Recent innovations in survey design include research on anticipating nonsampling errors at the design stage and development of balanced and adaptive sampling designs to take advantage of detailed sampling frame information or data gathered during the survey process. Nonparametric and machine learning methods are increasingly used for data editing as well as for model-assisted estimation and nonresponse adjustments. Small area models have been expanded to incorporate spatial and time series information, increase the flexibility and robustness of the linking and variance models, benchmark to large-area direct estimators, and (for unit level models) account for informative sampling designs. The increasing availability of large administrative datasets, sensor and satellite data, and convenience samples has spurred research on how to use these sources - on their own and when integrated with probability samples. We conclude by discussing some frontiers for survey research.
Release date: 2025-06-30
9. Comments by Mary E. Thompson on “Progress in survey science and practice: Yesterday-today-tomorrow”
Articles and reports: 12-001-X202500100016
Description: These comments on C.-E. Särndal’s paper, “Progress in survey science and practice: yesterday-today-tomorrow”, will touch on probability sampling fundamentals, progress through competing approaches to inference, connections with other parts of statistics, and data in the twenty-first century.
Release date: 2025-06-30
10. Fully synthetic data for complex surveys
Articles and reports: 12-001-X202400200008
Description: When seeking to release public use files for confidential data, statistical agencies can generate fully synthetic data. We propose an approach for making fully synthetic data from surveys collected with complex sampling designs. Our approach adheres to the general strategy proposed by Rubin (1993). Specifically, we generate pseudo-populations by applying the weighted finite population Bayesian bootstrap to account for survey weights, take simple random samples from those pseudo-populations, estimate synthesis models using these simple random samples, and release simulated data drawn from the models as public use files. To facilitate variance estimation, we use the framework of multiple imputation with two data generation strategies. In the first, we generate multiple data sets from each simple random sample. In the second, we generate a single synthetic data set from each simple random sample. We present multiple imputation combining rules for each setting. We illustrate the repeated sampling properties of the combining rules via simulation studies, including comparisons with synthetic data generation based on pseudo-likelihood methods. We apply the proposed methods to a subset of data from the American Community Survey.
Release date: 2024-12-20

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Analysis (112)

Analysis (112) (90 to 100 of 112 results)

91. Comparative Study of Analytical Consumer Price Indexes for Different Subgroups of the Reference Population Archived
Articles and reports: 62F0014M1998013
Geography: Canada
Description: The reference population for the Consumer Price Index (CPI) has been represented, since the 1992 updating of the basket of goods and services, by families and unattached individuals living in private urban or rural households. The official CPI is a measure of the average percentage change over time in the cost of a fixed basket of goods and services purchased by Canadian consumers.

Because of the broadly defined target population of the CPI, the measure has been criticised for failing to reflect the inflationary experiences of certain socio-economic groups. This study examines this question for three sub-groups of the reference population of the CPI. It is an extension of earlier studies on the subject done at Statistics Canada.

In this document, analytical consumer price indexes sub-group indexes are compared to the analytical index for the whole population calculated at the national geographic level.

The findings tend to point to those of earlier Statistics Canada studies on sub-groups in the CPI reference population. Those studies have consistently concluded that a consumer price index established for a given sub-group does not differ substantially from the index for the whole reference population.
Release date: 1999-05-13
92. Inverse sampling design algorithms Archived
Articles and reports: 12-001-X19970013101
Description:
In the main body of statistics, sampling is often disposed of by assuming a sampling process that selects random variables such that they are independent and identically distributed (IID). Important techniques, like regression and contingency table analysis, were developed largely in the IID world; hence, adjustments are needed to use them in complex survey settings. Rather than adjust the analysis, however, what is new in the present formulation is to draw a second sample from the original sample. In this second sample, the first set of selections are inverted, so as to yield at the end a simple random sample. Of course, to employ this two-step process to draw a single simple random sample from the usually much larger complex survey would be inefficient, so multiple simple random samples are drawn and a way to base inferences on them developed. Not all original samples can be inverted; but many practical special cases are discussed which cover a wide range of practices.
Release date: 1997-08-18
93. Variable selection for regression estimation in finite populations Archived
Articles and reports: 12-001-X19970013102
Description:
The selection of auxiliary variables is considered for regression estimation in finite populations under a simple random sampling design. This problem is a basic one for model-based and model-assisted survey sampling approaches and is of practical importance when the number of variables available is large. An approach is developed in which a mean squared error estimator is minimised. This approach is compared to alternative approaches using a fixed set of auxiliary variables, a conventional significance test criterion, a condition number reduction approach and a ridge regression approach. The proposed approach is found to perform well in terms of efficiency. It is noted that the variable selection approach affects the properties of standard variance estimators and thus leads to a problem of variance estimation.
Release date: 1997-08-18
94. A transformation method for finite population sampling calibrated with empirical likelihood Archived
Articles and reports: 12-001-X19960022980
Description:
In this paper, we study a confidence interval estimation method for a finite population average when some auxiliairy information is available. As demonstrated by Royall and Cumberland in a series of empirical studies, naive use of existing methods to construct confidence intervals for population averages may result in very poor conditional coverage probabilities, conditional on the sample mean of the covariate. When this happens, we propose to transform the data to improve the precision of the normal approximation. The transformed data are then used to make inference on the original population average, and the auxiliary information is incorporated into the inference directly, or by calibration with empirical likelihood. Our approach is design-based. We apply our approach to six real populations and find that when transformation is needed, our approach performs well compared to the usual regression method.
Release date: 1997-01-30
95. Fertility Projections for Canada, Provinces and Territories, 1993-2016 Archived
Articles and reports: 91F0015M1996001
Geography: Canada
Description:
This paper describes the methodology for fertility projections used in the 1993-based population projections by age and sex for Canada, provinces and territories, 1993-2016. A new version of the parametric model known as the Pearsonian Type III curve was applied for projecting fertility age pattern. The Pearsonian Type III model is considered as an improvement over the Type I used in the past projections. This is because the Type III curve better portrays both the distribution of the age-specific fertility rates and the estimates of births. Since the 1993-based population projections are the first official projections to incorporate the net census undercoverage in the population base, it has been necessary to recalculate fertility rates based on the adjusted population estimates. This recalculation resulted in lowering the historical series of age-specific and total fertility rates, 1971-1993. The three sets of fertility assumptions and projections were developed with these adjusted annual fertility rates.
It is hoped that this paper will provide valuable information about the technical and analytical aspects of the current fertility projection model. Discussions on the current and future levels and age pattern of fertility in Canada, provinces and territories are also presented in the paper.
Release date: 1996-08-02
96. Multiple sample estimation of population and census undercount in the presence of matching errors Archived
Articles and reports: 12-001-X199600114385
Description:
The multiple capture-recapture census is reconsidered by relaxing the traditional perfect matching assumption. We propose matching error models to characterize error-prone matching mechanisms. The observed data take the form of an incomplete 2^k contingency table with one missing cell and follow a multinomial distribution. We develop a procedure for the estimation of the population size. Our approach applies to both standard log-linear models for contingency tables and log-linear models for heterogeneity of catchability. We illustrate the method and estimation using a 1988 dress rehearsal study for the 1990 census conducted by the U.S. Bureau of the Census.
Release date: 1996-06-14
97. Design effects for correlated (P_i - P_j) Archived
Articles and reports: 12-001-X199500214398
Description:
We present empirical evidence from 14 surveys in six countries concerning the existence and magnitude of design effects (defts) for five designs of two major types. The first type concerns deft (p_i – p_j), the difference of two proportions from a polytomous variable of three or more categories. The second type uses Chi-square tests for differences from two samples. We find that for all variables in all designs deft (p_i – p_j) \cong [deft (p_i) + deft (p_j)] / 2 are good approximations. These are empirical results, and exceptions disprove the existence of mere analytical inequalities. These results hold despite great variations of defts between variables and also between categories of the same variables. They also show the need for sample survey treatment of survey data even for analytical statistics. Furthermore they permit useful approximations of deft (p_i – p_j) from more accessible deft (p_i) values.
Release date: 1995-12-15
98. Median estimation using auxiliary information Archived
Articles and reports: 12-001-X199500114408
Description:
The problem of estimating the median of a finite population when an auxiliary variable is present is considered. Point and interval estimators based on a non-informative Bayesian approach are proposed. The point estimator is compared to other possible estimators and is seen to perform well in a variety of situations.
Release date: 1995-06-15
99. Robust model-based methods for analytic surveys Archived
Articles and reports: 12-001-X199200214487
Description:
This paper reviews the idea of robustness for randomisation and model-based inference for descriptive and analytic surveys. The lack of robustness for model-based procedures can be partially overcome by careful design. In this paper a robust model-based approach to analysis is proposed based on smoothing methods.
Release date: 1992-12-15
100. Robustness and optimal design under prediction models for finite populations Archived
Articles and reports: 12-001-X199200214488
Description:
In many finite population sampling problems the design that is optimal in the sense of minimizing the variance of the best linear unbiased estimator under a particular working model is bad in the sense of robustness - it leaves the estimator extremely vulnerable to bias if the working model is incorrect. However there are some important models under which one design provides both efficiency and robustness. We present a theorem that identifies such models and their optimal designs.
Release date: 1992-12-15

Reference (8)

Reference (8) ((8 results))

1. The Potential Use of Remote Sensing to Produce Field Crop Statistics at Statistics Canada Archived
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
2. A note on identifiers in the National Longitudinal Survey of Children and Youth Archived
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
3. Survey of Financial Security - Methodology for Estimating the Value of Employer Pension Plan Benefits Archived
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
4. Survey of Financial Security - Estimating the Value of Employer Pension Plan Benefits - A Discussion Paper Archived
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
5. The challenges of using administrative data to support policy-relevant research: The example of the longitudinal immigration database (IMDB) Archived
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
6. The U.S. manufacturing plant ownership change database: Research possibilities Archived
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
7. Uncertainties in estimates of radon lung cancer risks Archived
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
8. A Comparison of Census Geographic Areas of Canada and the United States Archived
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:: 2026-09-12