Weighting and estimation

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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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Analysis (610)

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61. The missing information principle ‒ A paradigm for analysis of messy sample survey data
Articles and reports: 12-001-X202300200018
Description: Sample surveys, as a tool for policy development and evaluation and for scientific, social and economic research, have been employed for over a century. In that time, they have primarily served as tools for collecting data for enumerative purposes. Estimation of these characteristics has been typically based on weighting and repeated sampling, or design-based, inference. However, sample data have also been used for modelling the unobservable processes that gave rise to the finite population data. This type of use has been termed analytic, and often involves integrating the sample data with data from secondary sources.
Alternative approaches to inference in these situations, drawing inspiration from mainstream statistical modelling, have been strongly promoted. The principal focus of these alternatives has been on allowing for informative sampling. Modern survey sampling, though, is more focussed on situations where the sample data are in fact part of a more complex set of data sources all carrying relevant information about the process of interest. When an efficient modelling method such as maximum likelihood is preferred, the issue becomes one of how it should be modified to account for both complex sampling designs and multiple data sources. Here application of the Missing Information Principle provides a clear way forward.
In this paper I review how this principle has been applied to resolve so-called “messy” data analysis issues in sampling. I also discuss a scenario that is a consequence of the rapid growth in auxiliary data sources for survey data analysis. This is where sampled records from one accessible source or register are linked to records from another less accessible source, with values of the response variable of interest drawn from this second source, and where a key output is small area estimates for the response variable for domains defined on the first source.
Release date: 2024-01-03
62. Mapping Production Activity in Yukon: Experimental Indexes of Grid Square-based Gross Domestic Product
Articles and reports: 11-633-X2023003
Description: This paper spans the academic work and estimation strategies used in national statistics offices. It addresses the issue of producing fine, grid-level geography estimates for Canada by exploring the measurement of subprovincial and subterritorial gross domestic product using Yukon as a test case.
Release date: 2023-12-15
63. Combining data from surveys and related sources
Articles and reports: 12-001-X202300100003
Description: To improve the precision of inferences and reduce costs there is considerable interest in combining data from several sources such as sample surveys and administrative data. Appropriate methodology is required to ensure satisfactory inferences since the target populations and methods for acquiring data may be quite different. To provide improved inferences we use methodology that has a more general structure than the ones in current practice. We start with the case where the analyst has only summary statistics from each of the sources. In our primary method, uncertain pooling, it is assumed that the analyst can regard one source, survey r, as the single best choice for inference. This method starts with the data from survey r and adds data from those other sources that are shown to form clusters that include survey r. We also consider Dirichlet process mixtures, one of the most popular nonparametric Bayesian methods. We use analytical expressions and the results from numerical studies to show properties of the methodology.
Release date: 2023-06-30
64. Official Statistics based on the Dutch Health Survey during the Covid-19 Pandemic
Articles and reports: 12-001-X202300100004
Description: The Dutch Health Survey (DHS), conducted by Statistics Netherlands, is designed to produce reliable direct estimates at an annual frequency. Data collection is based on a combination of web interviewing and face-to-face interviewing. Due to lockdown measures during the Covid-19 pandemic there was no or less face-to-face interviewing possible, which resulted in a sudden change in measurement and selection effects in the survey outcomes. Furthermore, the production of annual data about the effect of Covid-19 on health-related themes with a delay of about one year compromises the relevance of the survey. The sample size of the DHS does not allow the production of figures for shorter reference periods. Both issues are solved by developing a bivariate structural time series model (STM) to estimate quarterly figures for eight key health indicators. This model combines two series of direct estimates, a series based on complete response and a series based on web response only and provides model-based predictions for the indicators that are corrected for the loss of face-to-face interviews during the lockdown periods. The model is also used as a form of small area estimation and borrows sample information observed in previous reference periods. In this way timely and relevant statistics describing the effects of the corona crisis on the development of Dutch health are published. In this paper the method based on the bivariate STM is compared with two alternative methods. The first one uses a univariate STM where no correction for the lack of face-to-face observation is applied to the estimates. The second one uses a univariate STM that also contains an intervention variable that models the effect of the loss of face-to-face response during the lockdown.
Release date: 2023-06-30
65. Comments by Jae Kwang Kim and HaiYing Wang on “Statistical disclosure control and developments in formal privacy: In memoriam to Chris Skinner”: A note on weight smoothing in survey sampling
Articles and reports: 12-001-X202300100005
Description: Weight smoothing is a useful technique in improving the efficiency of design-based estimators at the risk of bias due to model misspecification. As an extension of the work of Kim and Skinner (2013), we propose using weight smoothing to construct the conditional likelihood for efficient analytic inference under informative sampling. The Beta prime distribution can be used to build a parameter model for weights in the sample. A score test is developed to test for model misspecification in the weight model. A pretest estimator using the score test can be developed naturally. The pretest estimator is nearly unbiased and can be more efficient than the design-based estimator when the weight model is correctly specified, or the original weights are highly variable. A limited simulation study is presented to investigate the performance of the proposed methods.
Release date: 2023-06-30
66. An extension of the weight share method when using a continuous sampling frame
Articles and reports: 12-001-X202300100011
Description: The definition of statistical units is a recurring issue in the domain of sample surveys. Indeed, not all the populations surveyed have a readily available sampling frame. For some populations, the sampled units are distinct from the observation units and producing estimates on the population of interest raises complex questions, which can be addressed by using the weight share method (Deville and Lavallée, 2006). However, the two populations considered in this approach are discrete. In some fields of study, the sampled population is continuous: this is for example the case of forest inventories for which, frequently, the trees surveyed are those located on plots of which the centers are points randomly drawn in a given area. The production of statistical estimates from the sample of trees surveyed poses methodological difficulties, as do the associated variance calculations. The purpose of this paper is to generalize the weight share method to the continuous (sampled population) ? discrete (surveyed population) case, from the extension proposed by Cordy (1993) of the Horvitz-Thompson estimator for drawing points carried out in a continuous universe.
Release date: 2023-06-30
67. Multilevel time series modelling of antenatal care coverage in Bangladesh at disaggregated administrative levels
Articles and reports: 12-001-X202200200010
Description:
Multilevel time series (MTS) models are applied to estimate trends in time series of antenatal care coverage at several administrative levels in Bangladesh, based on repeated editions of the Bangladesh Demographic and Health Survey (BDHS) within the period 1994-2014. MTS models are expressed in an hierarchical Bayesian framework and fitted using Markov Chain Monte Carlo simulations. The models account for varying time lags of three or four years between the editions of the BDHS and provide predictions for the intervening years as well. It is proposed to apply cross-sectional Fay-Herriot models to the survey years separately at district level, which is the most detailed regional level. Time series of these small domain predictions at the district level and their variance-covariance matrices are used as input series for the MTS models. Spatial correlations among districts, random intercept and slope at the district level, and different trend models at district level and higher regional levels are examined in the MTS models to borrow strength over time and space. Trend estimates at district level are obtained directly from the model outputs, while trend estimates at higher regional and national levels are obtained by aggregation of the district level predictions, resulting in a numerically consistent set of trend estimates.

Release date: 2022-12-15
68. Optimal linear estimation in two-phase sampling
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
69. Bayesian spatial models for estimating means of sampled and non-sampled small areas
Articles and reports: 12-001-X202200200012
Description:
In many applications, the population means of geographically adjacent small areas exhibit a spatial variation. If available auxiliary variables do not adequately account for the spatial pattern, the residual variation will be included in the random effects. As a result, the independent and identical distribution assumption on random effects of the Fay-Herriot model will fail. Furthermore, limited resources often prevent numerous sub-populations from being included in the sample, resulting in non-sampled small areas. The problem can be exacerbated for predicting means of non-sampled small areas using the above Fay-Herriot model as the predictions will be made based solely on the auxiliary variables. To address such inadequacy, we consider Bayesian spatial random-effect models that can accommodate multiple non-sampled areas. Under mild conditions, we establish the propriety of the posterior distributions for various spatial models for a useful class of improper prior densities on model parameters. The effectiveness of these spatial models is assessed based on simulated and real data. Specifically, we examine predictions of statewide four-person family median incomes based on the 1990 Current Population Survey and the 1980 Census for the United States of America.

Release date: 2022-12-15
70. Market Basket Measure Technical Paper: The other necessities component
Articles and reports: 75F0002M2022006
Description:
This technical paper describes how the cost for "other necessities" is estimated in the 2018-base MBM. It provides a brief overview of the theory and application of techniques for estimating costs of "other necessities" in poverty lines and deconstructs the 2018-base MBM other necessities component to provide insights on how it is constructed. The aim of this paper is to provide a more detailed understanding of how the other necessities component of the MBM is estimated.

Release date: 2022-12-08

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