Weighting and estimation

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All (638)

All (638) (20 to 30 of 638 results)

21. On the use of machine learning methods for the treatment of unit nonresponse in surveys
Articles and reports: 12-001-X202500100003
Description: In recent years, there has been a significant interest in machine learning in national statistical offices. Thanks to their flexibility, these methods may prove useful at the nonresponse treatment stage. In this article, we conduct an empirical investigation in order to compare several machine learning procedures in terms of bias and efficiency. In addition to the classical machine learning procedures, we assess the performance of ensemble approaches that make use of different machine learning procedures to produce a set of weights adjusted for nonresponse.
Release date: 2025-06-30
22. 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
23. sCHAID: A tool for constructing nonresponse adjustment cells under a design-based framework
Articles and reports: 12-001-X202500100006
Description: Survey practitioners have increasingly embraced the benefits of modern machine learning techniques, including classification and regression tree algorithms, in the development of nonresponse adjustments. These methods, which do not require a predefined functional relationship between outcomes and predictors, offer a practical means of conducting variable selection and deriving interpretable structures that link response propensity with explanatory variables. However, when applying these algorithms to survey data, it is common to overlook crucial factors like sampling weights, as well as sample design features such as stratification and clustering. To bridge this shortcoming, we propose an extension of the Chi-square Automatic Interaction Detector (CHAID) approach, and we describe the design-based asymptotic properties of the resulting “survey CHAID” (sCHAID) method. To facilitate the practical use of sCHAID, we incorporate a Rao-Scott correction into the splitting criterion, accounting for the survey design. Using data from the U.S. American Community Survey, we illustrate the use of the method and evaluate its performance through comparisons with existing weighted and unweighted algorithms.
Release date: 2025-06-30
24. Model-assisted calibration estimation using generalized entropy calibration in survey sampling
Articles and reports: 12-001-X202500100007
Description: We introduce a novel approach to model-assisted calibration estimation in survey sampling using generalized entropy. The method builds upon recent work by Kwon, Kim and Qiu (2024) and extends it to a model-assisted framework. Unlike traditional calibration techniques, this approach employs a generalized entropy function as the objective for optimization and incorporates a debiasing calibration constraint to ensure design consistency. The proposed estimator is shown to be asymptotically equivalent to an augmented generalized regression (GREG) estimator. It allows for unequal model variance, potentially improving efficiency when the sampling design is informative. The paper presents both design-based and model-based justifications for the method, along with asymptotic properties and variance estimation techniques. Computational aspects are discussed, including an unconstrained optimization approach that facilitates implementation, especially for high-dimensional auxiliary variables. The method’s performance is evaluated through a simulation study, demonstrating its effectiveness in improving estimation efficiency, particularly when the sampling design is informative.
Release date: 2025-06-30
25. Use of nonprobability samples for official statistics, state of the art
Articles and reports: 12-001-X202500100008
Description: Tightened budgets, continuing decrease of response rates in traditional probability surveys and increasing pressure by users for more timely data, has stimulated research on the use of nonprobability sample data, such as administrative records, web scraping, mobile phone data and voluntary internet surveys, for inference on finite population parameters like means and totals. These data are often easier, faster and cheaper to collect than traditional probability samples. However, a major concern with the use of this kind of data for official statistics is their nonrepresentativeness due to possible selection bias, which if not accounted for properly, could bias the inference. In this article, we review and discuss methods considered in the literature to deal with this problem and propose new methods, distinguishing between methods based on integration of the nonprobability sample with an appropriate probability sample, and methods that base the inference solely on the nonprobability sample. Empirical illustrations, based on simulated data are provided.
Release date: 2025-06-30
26. Authors’ response to comments on “Trends and directions in sample survey theory and methods”
Articles and reports: 12-001-X202500100010
Description: The discussants highlight promising research topics for improving the quality and granularity of estimates from surveys. We agree that continued research is needed to evaluate models used for inference, and suggest development of measures of model dependence.
Release date: 2025-06-30
27. Comments by M. Giovanna Ranalli on “Trends and directions in sample survey theory and methods”
Articles and reports: 12-001-X202500100011
Description: This discussion examines some advancements in survey design and estimation, inspired by the comprehensive appraisal of Professors Jon Rao and Sharon Lohr on current trends in the field. It delves into three specific areas: balanced sampling, calibration, and small area estimation. Probabilistic balanced sampling methods, such as the cube method and penalized balanced sampling, are explored, with an emphasis on addressing emerging challenges, including extensions to linear mixed models, nonparametric regression models, and spatially balanced designs. Calibration is discussed using a modular framework that incorporates modern regression techniques, and highlights innovative uses of model calibration for data editing and causal inference. Small area estimation is considered in the context of latent variable modeling and data integration, emphasizing its role when the variable(s) of interest cannot be measured either directly or without error. Applications in integrating probability and non-probability data and conducting causal analysis at local level are also discussed.
Release date: 2025-06-30
28. Comments by Jean D. Opsomer, Daifeng Han and Medha Uppala on “Trends and directions in sample survey theory and methods”
Articles and reports: 12-001-X202500100012
Description: In this discussion, we complement the excellent overview by Profs. Lohr and Rao with some additional topics. The first topic is a call for more recognition of the central role of modeling in survey estimation. The second is a brief discussion of the use of partial frame information in survey design. Finally, we draw the attention to recent increases of synthetic methods, in particular, multilevel regression and poststratification (MRP) in small area estimation applications.
Release date: 2025-06-30
29. 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
30. Bayesian predictive inference of a finite population mean without specifying the relation between the study variable and the covariates
Articles and reports: 12-001-X202400200004
Description: While we avoid specifying the parametric relationship between the study variable and covariates, we illustrate the advantage of including a spatial component to better account for the covariates in our models to make Bayesian predictive inference. We treat each unique covariate combination as an individual stratum, then we use small area estimation techniques to make inference about the finite population mean of the continuous response variable. The two spatial models used are the conditional autoregressive and simple conditional autoregressive models. We include the spatial effects by creating the adjacency matrix via the Mahalanobis distance between covariates. We also show how to incorporate survey weights into the spatial models when dealing with probability survey data. We compare the results of two non-spatial models including the Scott-Smith model and the Battese, Harter, and Fuller model to the spatial models. We illustrate the comparison between the aforementioned models with an application using BMI data from eight counties in California. Our goal is to have neighboring strata yield similar predictions, and to increase the difference between strata that are not neighbors. Ultimately, using the spatial models shows less global pooling compared to the non-spatial models, which was the desired outcome.
Release date: 2024-12-20

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71. Attrition in the Longitudinal and International Study of Adults, Wave 1 (2012) to Wave 4 (2018)
Articles and reports: 89-648-X2022001
Description:
This report explores the size and nature of the attrition challenges faced by the Longitudinal and International Study of Adults (LISA) survey, as well as the use of a non-response weight adjustment and calibration strategy to mitigate the effects of attrition on the LISA estimates. The study focuses on data from waves 1 (2012) to 4 (2018) and uses practical examples based on selected demographic variables, to illustrate how attrition be assessed and treated.

Release date: 2022-11-14
72. Study: Attrition in the Longitudinal and International Study of Adults, Wave 1 (2012) to Wave 4 (2018) Archived
Stats in brief: 11-001-X202231822683
Description: Release published in The Daily – Statistics Canada’s official release bulletin
Release date: 2022-11-14
73. Bayesian inference for a variance component model using pairwise composite likelihood with survey data
Articles and reports: 12-001-X202200100002
Description: We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.
Release date: 2022-06-21
74. Relative performance of methods based on model-assisted survey regression estimation: A simulation study
Articles and reports: 12-001-X202200100003
Description:
Use of auxiliary data to improve the efficiency of estimators of totals and means through model-assisted survey regression estimation has received considerable attention in recent years. Generalized regression (GREG) estimators, based on a working linear regression model, are currently used in establishment surveys at Statistics Canada and several other statistical agencies. GREG estimators use common survey weights for all study variables and calibrate to known population totals of auxiliary variables. Increasingly, many auxiliary variables are available, some of which may be extraneous. This leads to unstable GREG weights when all the available auxiliary variables, including interactions among categorical variables, are used in the working linear regression model. On the other hand, new machine learning methods, such as regression trees and lasso, automatically select significant auxiliary variables and lead to stable nonnegative weights and possible efficiency gains over GREG. In this paper, a simulation study, based on a real business survey sample data set treated as the target population, is conducted to study the relative performance of GREG, regression trees and lasso in terms of efficiency of the estimators and properties of associated regression weights. Both probability sampling and non-probability sampling scenarios are studied.

Release date: 2022-06-21
75. Bayesian inference for multinomial data from small areas incorporating uncertainty about order restriction
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
76. A generalization of inverse probability weighting
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
77. Canadian Income Survey: Population rebasing, 2012 to 2019
Articles and reports: 75F0002M2022001
Description:
Periodically, income statistics are updated to reflect the most recent population estimates derived after the census. Accordingly, with the release of the 2020 data from the Canadian Income Survey (CIS), Statistics Canada has revised estimates for 2012 to 2019 using totals from population estimates based on the 2016 Census. This paper presents a comparison between revised and unrevised estimates for key income series, and describes other modifications made to CIS variables.

Release date: 2022-03-23
78. Two local diagnostics to evaluate the efficiency of the empirical best predictor under the Fay-Herriot model
Articles and reports: 12-001-X202100200001
Description:
The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.
Release date: 2022-01-06
79. With-replacement bootstrap variance estimation for household surveys Principles, examples and implementation
Articles and reports: 12-001-X202100200005
Description:
Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.
Release date: 2022-01-06
80. Replication variance estimation after sample-based calibration
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

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:: 2026-09-13