Weighting and estimation

Results

All (638)

All (638) (570 to 580 of 638 results)

571. Estimates based on randomly rounded data Archived
Articles and reports: 12-001-X198700214515
Description:
Methods are given to estimate functions of the cell probabilities associated with a table of multinomial data that has been randomly rounded to multiples of a given number, say l. We show that: (i) random rounding causes only second order effects on bias and variance; (ii) the loss of efficiency in using the natural estimates of cell probability is negligible provided that the cell entry is large compared with (l^2 - 1) / (6R) where R is the number of cells in the table; and (iii) estimates of apparently exponentially small bias are available for moments of these natural estimates and for polynomials in the cell probabilities.
Release date: 1987-12-15
572. Variance estimation for the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198700214516
Description:
The biases and stabilities of alternative variance estimators for the two stage random group design (Rao et al. 1962) are evaluated in a Monte Carlo study in the context of Canadian Labour Force Survey. The variance formula for raking ratio estimation procedure is derived using Taylor linearization method. The properties of the variance formula are investigated by a Monte Carlo simulation.
Release date: 1987-12-15
573. An alternative method of controlling Current Population Survey estimates to population counts Archived
Articles and reports: 12-001-X198700214605
Description:
The CPS uses raking ratio estimation in post-stratification estimation to adjust sample estimates of population to census-based estimates of the population. An alternative procedure, using generalized least squares, is compared to the current procedure.
Release date: 1987-12-15
574. A class of methods for using person controls in household weighting Archived
Articles and reports: 12-001-X198700214606
Description:
A class of “constrained minimum distance” methods is considered for constraining household weights to be consistent with auxiliary information on the number of persons in various age x race x sex cells. The constrained weights are as close as possible to the initial weights based on the inverse probability of selection. This class of methods includes raking and generalized least square methods, as well as multinomial maximum likelihood, (where the cells of the distribution are household types.) The properties of the methods in the presence of systematic undercoverage of the household types are studied through some simple models for coverage. Comparisons with the principal person method are made and the paper concludes with the observation that it is necessary to know more about the nature of survey undercoverage before deciding on which of the constrained minimum distance or principal person methods is to be preferred in applications.
Release date: 1987-12-15
575. An integrated method for weighting persons and families Archived
Articles and reports: 12-001-X198700214607
Description:
Household surveys generally use separate procedures for estimating characteristics of persons and those of families. An integrated procedure is proposed and a least-squares estimator introduced to achieve this end. The estimator is shown to be unbiased under certain general conditions. Using data from the Canadian Labour Force Survey, variances for the estimator are calculated and shown to compare favourably to those from current procedures.
Release date: 1987-12-15
576. Modified raking ratio estimation Archived
Articles and reports: 12-001-X198700214608
Description:
A hybrid technique is described that employs both conventional and raking ratio estimation to handle the case when the population frequencies N_ij in a two-dimensional table are known, but some of the observed frequencies n_ij are small (or zero). Results are provided on the approach taken as it has evolved in the Corporate Statistics of Income Program over the last several years. Changes are still being considered and these will be discussed as well.
Release date: 1987-12-15
577. Statistical properties of crop production estimators Archived
Articles and reports: 12-001-X198700114468
Description:
The National Agricultural Statistics Service, U.S. Department of Agriculture, conducts yield surveys for a variety of field crops in the United States. While field sampling procedures for various crops differ, the same basic survey design is used for all crops. The survey design and current estimators are reviewed. Alternative estimators of yield and production and of the variance of the estimators are presented. Current estimators and alternative estimators are compared, both theoretically and in a Monte Carlo simulation.
Release date: 1987-06-15
578. On efficient estimation of unemployment rates from Labour Force Survey Data Archived
Articles and reports: 12-001-X198700114510
Description:
The method of minimum Q^(T) estimation for complex survey designs proposed by Singh (1985) provides asymptotically efficient estimates of model parameters analogous to Neyman’s (1949) min X^2 estimation procedure for simple random samples. The Q^(T) can be viewed as a X^2 type statistic for categorical survey data, and min Q^(T) estimates provide a robust alternative to Weighted Least Squares estimates, which often display unstable behaviour for complex surveys. In this paper, the min Q^(T) method is first described and then illustrated for the problem of estimating parameters of a logit model for survey estimates of unemployment rates which are obtained from the October 1980 Canadian LFS data cross-classified according to age-education covariate categories. It is seen that the trace efficiency of smoothed estimates obtained by Kumar and Rao (1986), who applied the method of pseudo maximum likelihood estimates (pseudo mle) to the same problem can be slightly improved by the min Q^(T) method. Interestingly enough, pseudo mle for individual cells behave much the same way as the efficient min Q^(T) estimates for the particular LFS example.
Release date: 1987-06-15
579. A sampling procedure with inclusion probabilities proportional to size Archived
Articles and reports: 12-001-X198700114511
Description:
A new unequal probability sampling scheme for selecting n(> 2) units without replacement from a finite population is proposed. This scheme ensures that the inclusion probabilities are proportional to sizes. It has the advantage of simplicity in selection and estimation and also provides a non-negative variance estimator. The variance of the Horvitz-Thompson (H-T) estimator under the proposed scheme is shown to be smaller than that of the customary estimator in probability proportional to size sampling with replacement. The proposed scheme also compares favourably with the without replacement scheme suggested by Sampford (1967) in an empirical study on a few natural populations.
Release date: 1987-06-15
580. Comparison of estimators of population total in two-stage successive sampling using auxiliary information Archived
Articles and reports: 12-001-X198700114513
Description:
Singh and Srivastava (1973) proposed a linear unbiased estimator of the population mean when sampling on successive occasions using several auxiliary variables whose known population means remain unchanged for all occasions. In this paper, three composite estimators T_1, T_2 and T_3, each utilising an auxiliary variable whose known population mean changes from one occasion to the next, are presented for the estimation of the current population total. The proposed estimators are compared with the ordinary estimator, T_0, and the usual successive sampling estimator, T \prime, of the current population total without the use of auxiliary information. We find that using auxiliary information in conjunction with successive sampling does not always uniformly produce a gain in efficiency over T_0 or T \prime. However, when applied to a survey of teak plantations to estimate the mean height of teak trees, T_1, T_2 and T_3 proved more efficient than T_0 and T \prime.
Release date: 1987-06-15

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Analysis (610)

Analysis (610) (30 to 40 of 610 results)

31. A hierarchical gamma prior for modeling random effects in small area estimation
Articles and reports: 12-001-X202400200011
Description: Small area estimation (SAE) is becoming increasingly popular among survey statisticians. Since the direct estimates of small areas usually have large standard errors, model-based approaches are often adopted to borrow strength across areas. SAE models often use covariates to link different areas and random effects to account for the additional variation. Recent studies showed that random effects are not necessary for all areas, so global-local (GL) shrinkage priors have been introduced to effectively model the sparsity in random effects. The GL priors vary in tail behavior, and their performance differs under different sparsity levels of random effects. As a result, one needs to fit the model with different choices of priors and then select the most appropriate one based on the deviance information criterion or other evaluation metrics. In this paper, we propose a flexible prior for modeling random effects in SAE. The hyperparameters of the prior determine the tail behavior and can be estimated in a fully Bayesian framework. Therefore, the resulting model is adaptive to the sparsity level of random effects without repetitive fitting. We demonstrate the performance of the proposed prior via simulations and real applications.
Release date: 2024-12-20
32. Relaxed calibration of survey weights
Articles and reports: 12-001-X202400200012
Description: Population surveys are nowadays rarely analysed in isolation from any auxiliary information, often in the form of population counts, totals and other summaries. Calibration, or benchmarking, by which the weighted sample totals of auxiliary variables are matched to their (known) population totals, is widely applied. Methods for adjusting the weights to satisfy these constraints involve iterative procedures with unknown finite-sample properties. We develop an alternative method in which the weights are calibrated by minimising a quadratic function, requiring no iterations and yielding a unique solution. The relative priority of each constraint is represented by a tuning parameter. The properties of the weights and of the calibration estimator, as functions of these parameters, are explored analytically and by simulations. A connection of the proposed method with ridge calibration is established.
Release date: 2024-12-20
33. Inference from sampling with response probabilities estimated via calibration
Articles and reports: 12-001-X202400200013
Description: A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we highlight problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We present the results of a simulation study in order to illustrate these elements.
Release date: 2024-12-20
34. Design consistent random forest models for data collected from a complex sample
Articles and reports: 12-001-X202400200015
Description: Random forest models, which are the result of averaging the estimated values from a large number of tree models, represent a useful and flexible tool for modeling the data nonparametrically to provide accurately predicted values. There are many potential applications for these types of models when dealing with survey data. However, survey data is usually collected using an informative sample design, so it is necessary to have an algorithm for creating random forest models that account for this design during model estimation. The tree models used in the forest are typically obtained by estimating tree models on bootstrapped samples of the original data. Since the models depend on the observed data and the values observed in the sample depend on the informative sample design, the usual method for estimation is likely to lead to a biased random forest model when applied to survey data. In this article, we provide an algorithm and a set of conditions that produce consistent random forest models under an informative sample design and compare this method to the usual random forest modeling method. We show that ignoring the design can lead to biased model estimates.
Release date: 2024-12-20
35. Small Area Estimation Methodology Using Labour Force Survey Data
Articles and reports: 75-005-M2024003
Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.
Release date: 2024-09-17
36. Authors’ response to comments on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”: Some new developments on likelihood approaches to estimation of participation probabilities for non-probability samples
Articles and reports: 12-001-X202400100001
Description: Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.
Release date: 2024-06-25
37. Comments by Changbao Wu on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
Articles and reports: 12-001-X202400100002
Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.
Release date: 2024-06-25
38. Comments by Julie Gershunskaya and Vladislav Beresovsky on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
Articles and reports: 12-001-X202400100003
Description: Beaumont, Bosa, Brennan, Charlebois and Chu (2024) propose innovative model selection approaches for estimation of participation probabilities for non-probability sample units. We focus our discussion on the choice of a likelihood and parameterization of the model, which are key for the effectiveness of the techniques developed in the paper. We consider alternative likelihood and pseudo-likelihood based methods for estimation of participation probabilities and present simulations implementing and comparing the AIC based variable selection. We demonstrate that, under important practical scenarios, the approach based on a likelihood formulated over the observed pooled non-probability and probability samples performed better than the pseudo-likelihood based alternatives. The contrast in sensitivity of the AIC criteria is especially large for small probability sample sizes and low overlap in covariates domains.
Release date: 2024-06-25
39. Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data
Articles and reports: 12-001-X202400100004
Description: Non-probability samples are being increasingly explored in National Statistical Offices as an alternative to probability samples. However, it is well known that the use of a non-probability sample alone may produce estimates with significant bias due to the unknown nature of the underlying selection mechanism. Bias reduction can be achieved by integrating data from the non-probability sample with data from a probability sample provided that both samples contain auxiliary variables in common. We focus on inverse probability weighting methods, which involve modelling the probability of participation in the non-probability sample. First, we consider the logistic model along with pseudo maximum likelihood estimation. We propose a variable selection procedure based on a modified Akaike Information Criterion (AIC) that properly accounts for the data structure and the probability sampling design. We also propose a simple rank-based method of forming homogeneous post-strata. Then, we extend the Classification and Regression Trees (CART) algorithm to this data integration scenario, while again properly accounting for the probability sampling design. A bootstrap variance estimator is proposed that reflects two sources of variability: the probability sampling design and the participation model. Our methods are illustrated using Statistics Canada’s crowdsourcing and survey data.
Release date: 2024-06-25
40. Author’s response to comments on “Exchangeability assumption in propensity-score based adjustment methods for population mean estimation using non-probability samples”
Articles and reports: 12-001-X202400100005
Description: In this rejoinder, I address the comments from the discussants, Dr. Takumi Saegusa, Dr. Jae-Kwang Kim and Ms. Yonghyun Kwon. Dr. Saegusa’s comments about the differences between the conditional exchangeability (CE) assumption for causal inferences versus the CE assumption for finite population inferences using nonprobability samples, and the distinction between design-based versus model-based approaches for finite population inference using nonprobability samples, are elaborated and clarified in the context of my paper. Subsequently, I respond to Dr. Kim and Ms. Kwon’s comprehensive framework for categorizing existing approaches for estimating propensity scores (PS) into conditional and unconditional approaches. I expand their simulation studies to vary the sampling weights, allow for misspecified PS models, and include an additional estimator, i.e., scaled adjusted logistic propensity estimator (Wang, Valliant and Li (2021), denoted by sWBS). In my simulations, it is observed that the sWBS estimator consistently outperforms or is comparable to the other estimators under the misspecified PS model. The sWBS, as well as WBS or ABS described in my paper, do not assume that the overlapped units in both the nonprobability and probability reference samples are negligible, nor do they require the identification of overlap units as needed by the estimators proposed by Dr. Kim and Ms. Kwon.
Release date: 2024-06-25

Reference (28)

Reference (28) (0 to 10 of 28 results)

1. A Framework for Projecting Housing Use Associated with Immigrants and Non-Permanent Residents
Surveys and statistical programs – Documentation: 11-633-X2026002
Description: Recent changes in Canada’s immigration levels have heightened interest in understanding how immigration affects housing demand. This article develops a methodological framework for projecting housing use associated with permanent residents (PRs) and non-permanent residents (NPRs) under alternative immigration scenarios. The framework applies observed per capita housing use rates from the Census of Population to estimate incremental housing use by tenure over time.
Release date: 2026-04-24
2. Technical Guide on Demographic Estimates at Statistics Canada
Surveys and statistical programs – Documentation: 91-528-X
Description: The Technical Guide on Demographic Estimates at Statistics Canada provides detailed descriptions of the most current data sources and methods used by the Centre for demography at Statistics Canada to produce demographic estimates as part of the Demographic estimates program. They comprise postcensal and intercensal population estimates; base population; births and deaths; immigrants; emigrants; returning emigrants; non-permanent residents; interprovincial migration; subprovincial estimates of population and intraprovincial migration; population estimates by age and gender; and census family estimates. A glossary of commonly used terms is available at the end of the guide.
Release date: 2025-12-17
3. Sampling and Weighting Technical Report, Census of Population
Surveys and statistical programs – Documentation: 98-306-X
Description:
This report describes sampling, weighting and estimation procedures used in the Census of Population. It provides operational and theoretical justifications for them, and presents the results of the evaluations of these procedures.
Release date: 2023-10-04
4. Effective Income Tax and Transfer Rates: Technical Reference Note
Notices and consultations: 75F0002M2019006
Description:
In 2018, Statistics Canada released two new data tables with estimates of effective tax and transfer rates for individual tax filers and census families. These estimates are derived from the Longitudinal Administrative Databank. This publication provides a detailed description of the methods used to derive the estimates of effective tax and transfer rates.
Release date: 2019-04-16
5. Revisions to 2006 to 2011 income data Archived
Surveys and statistical programs – Documentation: 75F0002M2015003
Description:
This note discusses revised income estimates from the Survey of Labour and Income Dynamics (SLID). These revisions to the SLID estimates make it possible to compare results from the Canadian Income Survey (CIS) to earlier years. The revisions address the issue of methodology differences between SLID and CIS.
Release date: 2015-12-17
6. Methodology for measuring the underground economy by province and territory Archived
Surveys and statistical programs – Documentation: 13-605-X201500414166
Description:
Estimates of the underground economy by province and territory for the period 2007 to 2012 are now available for the first time. The objective of this technical note is to explain how the methodology employed to derive upper-bound estimates of the underground economy for the provinces and territories differs from that used to derive national estimates.
Release date: 2015-04-29
7. Sampling and Weighting Technical Report, National Household Survey, 2011 Archived
Surveys and statistical programs – Documentation: 99-002-X2011001
Description:
This report describes sampling and weighting procedures used in the 2011 National Household Survey. It provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.
Release date: 2015-01-28
8. Sampling and Weighting Technical Report, National Household Survey
Surveys and statistical programs – Documentation: 99-002-X
Description: This report describes sampling and weighting procedures used in the 2011 National Household Survey. It provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.
Release date: 2015-01-28
9. 2006 Census Technical Report: Sampling and Weighting
Surveys and statistical programs – Documentation: 92-568-X
Description:
This report describes sampling and weighting procedures used in the 2006 Census. It reviews the history of these procedures in Canadian censuses, provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.
Release date: 2009-08-11
10. Improvements in 2006 to the Labour Force Survey (LFS) Archived
Surveys and statistical programs – Documentation: 71F0031X2006003
Description:
This paper introduces and explains modifications made to the Labour Force Survey estimates in January 2006. Some of these modifications include changes to the population estimates, improvements to the public and private sector estimates and historical updates to several small Census Agglomerations (CA).
Release date: 2006-01-25

Date modified:: 2026-09-12