Weighting and estimation

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All (638)

All (638) (10 to 20 of 638 results)

11. Improved small area inference from data integration using global-local priors
Articles and reports: 12-001-X202500200009
Description: We present and apply methodology to improve inference for small area parameters by using data from several sources. This work extends Cahoy and Sedransk (2023) who showed how to integrate summary statistics from several sources. Our methodology uses hierarchical global-local prior distributions to make inferences for the proportion of individuals in Florida’s counties who do not have health insurance. Results from an extensive simulation study show that this methodology will provide improved inference by using several data sources. Among the five model variants evaluated the ones using horseshoe priors for all variances have better performance than the ones using lasso priors for the local variances.
Release date: 2025-12-23
12. Performance of hierarchical Bayes small area estimators using noninformative and informative priors with an application to the Canadian Labor Force Survey
Articles and reports: 12-001-X202500200010
Description: In this paper, we study the performance of hierarchical Bayes (HB) small area estimators using noninformative and informative priors. We apply the Bayesian models of You and Chapman (2006) and You (2021) to the Canadian Labor Force Survey (LFS) data and evaluate the impact of the priors on the HB estimators. A Bayesian model comparison and simulation study are also conducted. Our results indicate that a correct informative prior can lead to very good results, and noninformative priors can also perform very well. Incorrect informative priors can lead to poor results in terms of large bias and large coefficient of variation (CV). Noninformative priors are recommended in practice for HB small area estimation unless correctly specified informative priors are available. Informative priors are particularly useful when the number of small areas is relatively small.
Release date: 2025-12-23
13. Approximate hierarchical Bayes small area estimation using Natural Exponential Family with Quadratic Variance Function and poststratification
Articles and reports: 12-001-X202500200011
Description: We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function (NEF-QVF) in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.
Release date: 2025-12-23
14. Modified observed best prediction strategies for small area estimation with unit-level data
Articles and reports: 12-001-X202500200012
Description: The observed best prediction (OBP) under a nested-error regression (NER) model was previously proposed using a design-based mean squared prediction error (MSPE) as a tool to derive the best predictive estimator (BPE). A recent study showed the OBP under the NER model may suffer from numerical instability when computing the BPE. We propose several modifications of the OBP under the NER model, including ones using a model-based MSPE to derive the BPE, to improve the numerical stability and predictive performance. We compare the performance of the modified OBP strategies with the existing methods in a simulation study. A real-data example is discussed.
Release date: 2025-12-23
15. 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
16. Reverse-Engineering a Hypothetical Raking Process for the Estimation of Mean Squared Error of Raked Small Area Estimates Archived
Articles and reports: 11-522-X202500100006
Description: Small area estimation is frequently used to produce estimates at a disaggregated level where direct survey estimation does not have sufficient sample to produce precise estimates. Often this is done using the area-level Fay-Herriot model, by assuming the direct estimates are independent under the design and have a known variance, and applying a smoothing process to the variance estimates of the direct estimates to better meet that last assumption. It is not rare that small area estimates are benchmarked/raked to aggregated level direct estimates. This article shows that wrongly assuming independence can have a big impact on the MSE of the raked estimates. Values of the covariances between direct estimates are thus required for good point and MSE estimates. Getting good estimates of those covariances is difficult given the small sample sizes in some areas. An original way of deriving values for those covariances, by reverse-engineering a hypothetical raking process, is presented.
Release date: 2025-09-08
17. Correcting Selection Bias in a Non-probability Two-phase Payment Survey Archived
Articles and reports: 11-522-X202500100007
Description: This paper employs the Pseudo Maximum Likelihood (PML) estimator to the non-probability two-phase sampling when relevant auxiliary information is available from both probability survey sample and non-probability survey sample. To accommodate various weight adjustments and estimates variance beyond totals and means such as medians and quantiles, a simplified pseudo-population bootstrap procedure is proposed to approximately estimate the second-phase variance. Specifically, the simplification ignores the second phase sampling variability (i.e., treated as fixed, while in fact it is random), if the first-phase sampling fraction of the non-probability sample is negligible. Using the Bank of Canada 2020 Cash Alternative Survey Wave 2, the performance of the proposed method is compared to alternative methods, which either do not explicitly model the selection probability (i.e., raking) or ignore the valuable information from Phase 1 (i.e., Phase-2-Only). The results show that the PML-based approach performs better than raking and Phase-2-Only estimates in terms of reducing the selection bias for both phases' payment-related variables, especially for the low-response youth group. Estimated variances of the PML-based estimates are stable.

Release date: 2025-09-08
18. A Bias Evaluation for Probabilistic Web Panels at Statistics Canada Archived
Articles and reports: 11-522-X202500100009
Description: Three series of web panels were implemented at Statistics Canada from 2020 to 2024. Participants for these web panel series were recruited from respondents of large probabilistic social surveys (recruitment surveys), and subsequently were invited to complete a series of short online surveys. Estimates of recruitment survey variables were calculated using both recruitment survey weights and web panel weights, and these were compared; differences signal the possibility of residual bias that was not corrected by the web panel weighting process. This investigation found more significant differences than would be expected if the web panel estimator fully corrected for the bias resulting from the web panel response process. Questions related to certain topics such as politics and voting, sense of belonging, and media consumption were found to have the most significant differences between web panel estimates and recruitment survey estimates.
Release date: 2025-09-08
19. Data-driven Imputation Strategies and their Associated Quality Indicators in Economic Surveys Archived
Articles and reports: 11-522-X202500100011
Description: The use of modern "data"-driven imputation methods to treat non-response in the context of surveys processed in the Integrated Business Statistics Program at Statistics Canada has previously been explored. It was observed that these methods can lead to high quality imputation and further have the potential to result in broad efficiencies when setting up a particular survey's edit and imputation strategy. However, estimation of the associated total variance, more specifically the component due to imputation, remains a challenge. In this article, two methods for estimation of total variance are proposed and show preliminary results that have motivated us to pursue further research in this area.
Release date: 2025-09-08
20. Exploration of Approaches to Small Area Estimation with Measurement Errors and their Application to Indonesian Household Surveys Archived
Articles and reports: 11-522-X202500100028
Description: The United Nations Sustainable Development Goals require detailed, disaggregated data, typically obtained through household surveys. However, surveys alone cannot meet these needs for granular statistics. To address this, National Statistical Institutes adopt small area methods, but these face challenges as auxiliary variables, often derived from surveys, introduce measurement errors into the models. The aim is the application of measurement error correction in classic Fay-Herriot area-level model. The results demonstrate the robustness of the standard approach and ignoring measurement error but show there are specific scenarios where correction for measurement errors is beneficial. The approach is applied to a case study utilizing Indonesian household survey data.
Release date: 2025-09-08

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Analysis (610)

Analysis (610) (600 to 610 of 610 results)

601. Some estimators of population totals from simple random samples containing large units Archived
Articles and reports: 12-001-X197700100006
Description: The problem considered is the estimation of population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators which alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the variance of the usual estimator of the population total to the mean square error of these estimators. An empirical study of these estimators is also discussed.
Release date: 1977-06-20
602. Stratification index: Methodology and analysis Archived
Articles and reports: 12-001-X197600200002
Description: To obtain estimates of means or totals for a universe, a sample of units is often drawn to represent the universe and these units are then surveyed. One of the most important procedures used in the selection of the units is that of stratification, whereby the universe is split up into strata and independent samples of units are drawn from each stratum. A stratification index is developed to indicate the approximate fractional reduction in the sampling variance from that which would result if no stratification were undertaken. Also the methodology is extended to examine the effect of stratification on the sampling variance at different levels of stratification through the concept of a summary index. The stratification index is also extended to the case of ratio estimates using independent source data to re-weight the sample data. The index has been applied to the Canadian Labour Force Survey (LFS), a typical multi-stage stratified sample where ratio estimation, using projected age-sex population estimates is applied and empirical data are presented and analyzed.
Release date: 1976-12-13
603. The estimation of total variance in the 1976 Census Archived
Articles and reports: 12-001-X197600200004
Description: Published reports for the 1976 Census will include estimates of Total Variance as indicators of the reliability of the figures in these reports. In order to obtain these estimates of Total Variance, an Interpenetrating Design Experiment was incorporated into the collection methods for a sample of enumeration areas. In this paper we derive the formula for Total Variance in terms of variances due to sampling, correlated response and simple response. We then show how the Total Variance, and its components, can be estimated from the design and we give the estimators that will be used for the 1976 Census. The estimates of sampling and correlated response variance are unbiased but the simple response variance estimate is not.
Release date: 1976-12-13
604. Raking ratio estimators Archived
Articles and reports: 12-001-X197600100003
Description: This paper presents large sample results for the bias and variance of raking-ratio estimators for up to four iterations. Estimators of the bias and variance are also presented. An expression for the asymptotic covariance matrix of the maximum likelihood estimators of the cell proportions in a two-way table with known marginals is also given.
Release date: 1976-06-14
605. On the improvement of sample survey estimates Archived
Articles and reports: 12-001-X197500254830
Description: This paper focuses on the improvement of sample survey estimates in the particular situation where the survey sample, or part of it, is included in a larger sample from which auxiliary information is available. The properties of a method of estimation - sometimes applied in specific circumstances - are investigated and the limitations of its application are found. The application of the method to rotation designs in continuing surveys is more closely studied in the context of composite estimation.
Release date: 1975-12-15
606. On a ratio estimate with post-stratified weighting Archived
Articles and reports: 12-001-X197500254832
Description: A ratio estimate based on an auxiliary variable is considered for the case when the sample is post-stratified using information on another auxiliary variable. The variance of the ratio estimate is derived by the method of linearization [3,4]. An application to subprovincial estimation in the Canadian Labour Force Survey is discussed.
Release date: 1975-12-15
607. Measurement of response errors in Censuses and sample surveys Archived
Articles and reports: 12-001-X197500254824
Description:
Madow [1968] has proposed a two-phase sampling scheme under which response bias can be eliminated from sample surveys by obtaining “true” values for a subsample of the original sample. Often in cases of Censuses or ongoing surveys, the subsample data are not used to correct the main survey estimates but to assess their reliability. The main purpose of this paper is to present methods by which reliability estimates can be obtained when true values can be determined for a subsample of units.
Release date: 1975-12-15
608. The development of an automated estimation system Archived
Articles and reports: 12-001-X197500100001
Description: Although a survey is designed to satisfy a specific set of survey constraints, some steps involved in designing a survey, such as stratification, sample allocation and sample selection are common to all surveys. The steps involved in the creation of survey design systems are to identify, develop and implement common methods and procedures for such stages which, when taken together, constitute a survey design. The paper describes some methodological considerations in the development of an automated system for three methods of ratio estimation.
Release date: 1975-06-16
609. Some estimators for domain totals Archived
Articles and reports: 12-001-X197500100004
Description: A major concern in large scale surveys is the problem of sub-population estimation (domain estimation). This paper presents a study of four estimators for estimating domain totals. The domain considered in the study is an area type of domain, that is, a domain consisting of a combination of a certain number of area units belonging to different strata. This paper uses some actual data and some fictitious data to compare variances and mean square errors of the four estimators.
Release date: 1975-06-16
610. Components of variance model in multi-stage stratified samples Archived
Articles and reports: 12-001-X197500100007
Description: There are several multi-stage sample designs in various countries, such as the Current Population Survey in U.S.A., Labour Survey in Sweden, and the General Household Survey in United Kingdom. From each survey, estimated totals of Employed, Unemployed, and other characteristics may be obtained.
The Canadian Labour Force Survey is a monthly household survey in which the dwelling is the ultimate unit of sampling requiring two to four stages of selection. Each province is split up into strata and sampling units at various stages so that the sampling variance contains up to four components of variance whose actual formulae and estimation formulae are derived, utilizing those formerly derived by Yates and Grundy [12]. Ratio estimation is employed and the formulas are modified accordingly. To analyze the components of variance, it is necessary to express them in terms of components of sampling ratios and the sizes of sampling units at the various stages at provincial and national levels and approximate variance functions are thus derived.
Release date: 1975-06-16

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