Weighting and estimation

Results

All (638)

All (638) (590 to 600 of 638 results)

591. 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
592. 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
593. 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
594. 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
595. 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
596. 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
597. 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
598. 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
599. An empirical study of some regression estimators for small domains Archived
Articles and reports: 12-001-X198500114367
Description:
The synthetic estimator (SYN) has been traditionally used to estimate characteristics of small domains. Although it has the advantage of a small variance, it can be seriously biased in some small domains which depart in structure from the overall domains. Särndal (1981) introduced the regression estimator (REG) in the context of domain estimation. This estimator is nearly unbiased, however, it has two drawbacks; (i) its variance can be considerable in some small domains and (ii) it can take on negative values in situations that do not allow such values.
In this paper, we report on a compromise estimator which strikes a balance between the two estimators SYN and REG. This estimator, called the modified regression estimator (MRE), has the advantage of a considerably reduced variance compared to the REG estimator and has a smaller Mean Squared Error than the SYN estimator in domains where the latter is badly biased. The MRE estimator eliminates the drawback with negative values mentioned above. These results are supported by a Monte Carlo study involving 500 samples.
Release date: 1985-06-14
600. Post ‘81 censal redesign of the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198400214353
Description:
Following each decennial population census, the Canadian Labour Force Survey (CLFS) has undergone a sample redesign to reflect changes in population characteristics and to respond to changes in information needs. The current redesign program which culminated with introduction of a new sample at the beginning of 1985 included extensive research into improved sample design, data collection and estimation methodologies, highlights of which are described.
Release date: 1984-12-14

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Analysis (610)

Analysis (610) (10 to 20 of 610 results)

11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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

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