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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Analysis (610)

Analysis (610) (560 to 570 of 610 results)

561. Estimation of total for two characters in multiple frame surveys Archived
Articles and reports: 12-001-X198500214374
Description:
In this paper estimation of multiple characters in multiple frame surveys has been investigated. The gain due to two character study in a common survey, over separate surveys for individual characters, has been obtained. Cost comparison is also made between two character multi frame survey and two character single frame survey.
Release date: 1985-12-16
562. Use of administrative data files for migration estimates: A case study of driver’s licence file in Ontario Archived
Articles and reports: 12-001-X198500214379
Description:
In Canada, provincial and federal demographers have attempted to use various sets of administrative data to estimate migration flows. This paper presents the development of intra-provincial migration estimates using driver’s licence data in Ontario. An evaluation of these migration estimates has been carried out by comparing with those derived from the income tax data by Statistics Canada. Both files provide equally good and complimentary estimates of intra-provincial migration.
Release date: 1985-12-16
563. The development of Alberta Health Care records and their application to small-area population estimates Archived
Articles and reports: 12-001-X198500214380
Description:
This paper examines the use of administrative files from Alberta’s Health Care Insurance Plans combined with Vital Statistics data as inputs for estimating population. Results, which are presented and compared with Census data, indicate that Health Care data can be used to produce accurate population estimates at the provincial level and for smaller areas such as census divisions and municipalities.
Release date: 1985-12-16
564. The use of Hydro accounts in the British Columbia regression based population estimation model Archived
Articles and reports: 12-001-X198500214400
Description:
The accuracy of small area population estimates derived from a regression based model is heavily dependent on the ability of the indicator data selected to accurately reflect population change. Hence, prior knowledge as to the characteristics of the administrative data used as potential population indicators in a regression model is important. This report summarizes the strengths and weaknesses associated with the use of residential hydro accounts in the British Columbia regression based population estimation model.
Release date: 1985-12-16
565. Estimating the age/sex distribution of small area populations Archived
Articles and reports: 12-001-X198500214401
Description:
This paper describes a method of producing current age/sex specific population estimates for small areas utilizing as inputs total population estimates, birth and death data and estimates of historical residual net migration. An evaluation based on the 1981 Census counts for census divisions and school districts in British Columbia is presented.
Release date: 1985-12-16
566. Estimating population by age and sex for census divisions and census metropolitan areas Archived
Articles and reports: 12-001-X198500214402
Description:
A methodology has been developed for producing population estimates by single years of age and sex for small areas (census divisions and census metropolitan areas). To assure reliability, the estimates by single years of age are grouped into five years and only these grouped data are recomended for dissemination. They are based on the age-sex composition of population from the last census, births by sex, deaths by single years of age and sex, estimates of migration by age and sex, and counts of family allowance recipients in the age group 1-14 years.
Release date: 1985-12-16
567. Experience with small area population estimates Archived
Articles and reports: 12-001-X198500214403
Description:
Statistics Canada’s current methodologies forestimating the population of census divisions and census metropolitan areas are the regression-nested and component methods. This paper presents the experience with these estimates for the period 1981 to 1985, focusing on problems encountered with the input data on family allowance recipients.
Release date: 1985-12-16
568. Some aspects of nonresponse adjustments Archived
Articles and reports: 12-001-X198500114359
Description: Unit and item nonresponse almost always occur in surveys and censuses. The larger its size the larger its potential effect will be on survey estimates. It is, therefore, important to cope with it at every stage where they can be affected. At varying degrees the size of nonresponse can be coped with at design, field and processing stages. The nonresponse problems have an impact on estimation formulas for various statistics as a result of imputations and weight adjustments along with survey weights in the estimates of means, totals, or other statistics. The formulas may be decomposed into components that include response errors, the effect of weight adjustment for unit nonresponse, and the effect of substitution for nonresponse. The impacts of the design, field, and processing stages on the components of the estimates are examined.
Release date: 1985-06-14
569. Conditional inference in survey sampling Archived
Articles and reports: 12-001-X198500114364
Description:
Conventional methods of inference in survey sampling are critically examined. The need for conditioning the inference on recognizable subsets of the population is emphasized. A number of real examples involving random sample sizes are presented to illustrate inferences conditional on the realized sample configuration and associated difficulties. The examples include the following: estimation of (a) population mean under simple random sampling; (b) population mean in the presence of outliers; (c) domain total and domain mean; (d) population mean with two-way stratification; (e) population mean in the presence of non-responses; (f) population mean under general designs. The conditional bias and the conditional variance of estimators of a population mean (or a domain mean or total), and the associated confidence intervals, are examined.
Release date: 1985-06-14
570. Cost-variance optimization for the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198500114365
Description:
The cost-variance optimization of the design of the Canadian Labour Force Survey was carried out in two steps. First, the sample designs were optimized for each of the two major area types, the Self-Representing (SR) and the Non-Self-Representing (NSR) areas. Cost models were developed and parameters estimated from a detailed field study and by simulation, while variances were estimated using data from the Census of Population. The scope of the optimization included the allocation of sample to the two stages in the SR design, and the consideration of two alternatives to the old design in NSR areas. The second stage of optimization was the allocation of sample to SR and NSR areas.
Release date: 1985-06-14

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