Weighting and estimation

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All (638) (60 to 70 of 638 results)

61. Comments by Marc Christine on “Jean-Claude Deville’s contributions to survey theory and official statistics”
Articles and reports: 12-001-X202300200015
Description: This article discusses and provides comments on the Ardilly, Haziza, Lavallée and Tillé’s summary presentation of Jean-Claude Deville’s work on survey theory. It sheds light on the context, applications and uses of his findings, and shows how these have become engrained in the role of statisticians, in which Jean-Claude was a trailblazer. It also discusses other aspects of his career and his creative inventions.
Release date: 2024-01-03
62. Comments by Guillaume Chauvet on “Jean-Claude Deville’s contributions to survey theory and official statistics”
Articles and reports: 12-001-X202300200016
Description: In this discussion, I will present some additional aspects of three major areas of survey theory developed or studied by Jean-Claude Deville: calibration, balanced sampling and the generalized weight-share method.
Release date: 2024-01-03
63. 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
64. 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
65. 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
66. 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
67. 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
68. 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
69. 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
70. 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

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1. Exact and approximation formulas for second-order inclusion probabilities in randomized systematic sampling with unequal probabilities and without replacement
Articles and reports: 12-001-X202600100003
Description: Probability-proportional-to-size sampling is widely used by national statistical offices. Here population units are selected with probabilities proportional to an auxiliary variable. Variance formulas in such designs require both first- and second-order inclusion probabilities. The computation of second-order inclusion probabilities is particularly challenging for large populations, and has been the subject of extensive research. This article presents some new exact and approximation formulas for second-order inclusion probabilities in randomized systematic sampling with unequal probabilities and without replacement.
Release date: 2026-06-29
2. Improving the coverage of confidence intervals with respect to degrees of freedom: Application to the Canadian Census
Articles and reports: 12-001-X202600100005
Description: Confidence intervals are very often constructed based on a probability distribution that uses a certain number of degrees of freedom as a parameter. This is the case with the Student and the modified Wilson confidence intervals, discussed in this article, which use quantiles from the Student distribution where the number of degrees of freedom is generally unknown. For the length of a confidence interval to be representative of the reliability of an estimate, the actual coverage rate must match the nominal rate. To that end, the number of degrees of freedom in the probability distribution used in practice to calculate the confidence interval must be estimated as precisely as possible. An approximate rule is often used, although it tends to overestimate the actual number of degrees of freedom. In this article, a more precise version of degrees of freedom, derived from the Satterthwaite approximation, is obtained in the context of the Canadian Census of Population. The sampling design is equivalent to a simple random design without replacement, cluster-stratified, and the variance estimation method is an adaptation of the balanced repeated replication method. An explicit expression of the degrees of freedom is obtained under these conditions, enabling the factors influencing them to be identified. For comparison, the degree of freedom formula is also established for the conventional variance estimator. A simulation study shows that using this version of degrees of freedom corrects the undercoverage problem observed with the approximate rule, showing the importance of accurately assessing this number.
Release date: 2026-06-29
3. The inverse-variance trap: A simple ratio fix for combining skewed data
Articles and reports: 12-001-X202600100009
Description: Combining estimates from independent surveys via inverse-variance weights can lead to negative bias when unknown variances are estimated and the target variable is non-negative and positively skewed. In such cases, strong positive correlations typically arise between the estimators and their corresponding variance estimators, causing standard linear combinations with inverse-variance weights to exhibit negative bias. We introduce a strikingly simple method to reduce bias: replace the standard weight with the ratio of the estimator to the variance estimator. Under a linear model linking the two, we show that the new ratio-weighted estimator is approximately unbiased, whereas the conventional inverse-variance combination exhibits downward bias. Through simulations, we demonstrate that the new method brings both the bias and the mean squared error closer to the optimum for a wide range of different target variables. As our method uses only standardly reported summary statistics, it can be immediately adopted to reduce this widespread bias and improve the reliability of scientific findings in various fields.
Release date: 2026-06-29
4. Variance of the generalized regression estimator under measurement error
Articles and reports: 12-001-X202600100010
Description: With the exception of two-phase sampling, the standard variance approximation of the generalized regression (GREG) estimator assumes that the population totals in the weighting scheme are observed without error. If the weighting model of the GREG estimator contains population totals that are observed with measurement error sources other than the sampling error of first-phase estimates, then this uncertainty will be ignored by the variance approximation of the GREG estimator. This paper proposes a variance approximation for the GREG estimator that accounts for additional uncertainty arising from measurement error in one or more of the population totals used in the weighting scheme. This approach has been developed for, and is being applied to, the Dutch Labour Force Survey (DLFS). The monthly publications of the DLFS are obtained with a time series model, which corrects for rotation group bias and discontinuities caused by major redesigns and the loss of face-to-face interviews during COVID-19. The GREG estimates for the quarterly figures are benchmarked to the average of the monthly publications to enforce numerical consistency between monthly and quarterly publication tables. The standard variance approximation of the GREG estimator assumes that these population totals are observed without error. This results in an underestimation of the variance of the GREG estimator. The variance approximation proposed in this paper results in more realistic standard errors for the quarterly GREG estimates.
Release date: 2026-06-29
5. Bayesian differential privacy for small counties and individual commodities
Articles and reports: 12-001-X202600100011
Description: We construct a hybrid Bayesian method, which includes a differentially private mechanism, to mask Census county totals for a U.S. state on acreage of a commodity. We use surrogates for data collected at the farm level from a past U.S. Census of Agriculture to illustrate our procedure. We use two Bayesian small area models (parametric and mixture) to accommodate the smaller counties with fewer farms and some counties with large acres. In these models, the Laplace distribution provides a differentially private mechanism. In pre-processing, we also incorporate the Census weights to form the observed total acreage, a scaling factor to the Laplace mechanism for each county, a square-root transformation of the observed total acreage to avoid negative masked estimates especially for small counties, and the p-percent rule and the 3+ rule to partition the counties into suppressed counties, non-sensitive counties and sensitive counties. Because of difficulties in specifying and tuning the privacy budget (an unknown parameter), to balance security and utility, we specify a prior for the privacy budget, where the values are not specified, and the Gibbs sampler is used to fit the hierarchical Bayesian models. In post-processing, we use Bayesian predictive inference to obtain masked county acreages, and this includes a benchmarking so that the masked state total matches the observed state total. As a measure of reliability of the Bayesian procedure, we use the posterior coefficients of variation for the masked posterior means of the counties. As a measure of utility, we use the absolute relative errors for the individual counties, together with other global measures. For the sensitive counties, there are some differences between the two small area models but both are much better than an individual area model; the mixture model being the best compromise for security and utility.
Release date: 2026-06-29
6. Small area estimation of general indicators in off-census years
Articles and reports: 12-001-X202600100012
Description: We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a larger unit-level survey that adequately covers the areas of interest and contains the values of useful auxiliary variables. However, the minimal data requirement of the proposed method is a single survey with microdata on the target variable and suitable auxiliary variables for the period of interest. We also develop an estimator of the mean squared error (MSE) that accounts for the uncertainty introduced by the large survey used to replace the census of auxiliary information. Our empirical results indicate that the proposed predictors perform clearly better than the alternative predictors when census data are outdated, and are very close to optimal ones when census data are correct. They also illustrate that the proposed total MSE estimator corrects for the bias of purely model-based MSE estimators that do not account for the large survey uncertainty.
Release date: 2026-06-29
7. Effects of model misspecification on small area estimators
Articles and reports: 12-001-X202500200001
Description: Nested error regression models are commonly used to incorporate unit specific auxiliary variables to improve small area estimates. When the mean structure of the model is misspecified, the design-based mean squared prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP) generally increases. The Observed Best Prediction (OBP) method has been proposed with the intent to improve on the design-based MSPE over EBLUP. In this paper, we conduct a Monte Carlo simulation experiments to understand the effect of misspsecification of mean structures on different small area estimators. Our findings suggest that the OBP using unit-level auxiliary variables does not outperform the EBLUP in terms of design-based MSPE, unless the number of small areas m is extremely large. Conversely, the performance of OBP significantly improves when area-level auxiliary variables are employed. This paper includes both analytical and numerical evidence to demonstrate these observations, providing practical insights for addressing model misspecification in small area estimation (SAE).
Release date: 2025-12-23
8. Estimating monthly indicators for Consumer Confidence using Structural Time Series Models
Articles and reports: 12-001-X202500200003
Description: In this paper a model-based inference procedure based on a multivariate structural time series model is developed for the production of monthly figures about consumer confidence. The input for the model are five series of direct estimates for the indices that measure consumer confidence, which are derived from the Dutch Consumer Survey. The model improves the accuracy of the direct estimates, since it provides a better separation of measurement errors and sampling errors from estimated target parameters. The standard errors for the month-to-month changes are clearly smaller under the time series model. A second problem addressed in this paper is related to the transition to a new survey process in 2017. Structural time series models in combination with a parallel run are applied to estimate discontinuities induced by the redesign. An algorithm designed for the consumer confidence variables is developed to construct uninterrupted input series for the aforementioned structural time series model. This inference method facilitated a smooth transition to a new survey design and resulted in uninterrupted series about consumer confidence that date back to 1986. The method is implemented for the production of official monthly figures on consumer confidence in the Netherlands.
Release date: 2025-12-23
9. Quantile balancing inverse probability weighting for non-probability samples
Articles and reports: 12-001-X202500200005
Description: The use of non-probability data sources for statistical purposes and for official statistics has become increasingly popular in recent years. However, statistical inference based on non-probability samples is made more difficult by nature of their biasedness and lack of representativity. In this paper we propose quantile balancing inverse probability weighting estimator (QBIPW) for non-probability samples. We apply the idea of Harms and Duchesne (2006) allowing the use of quantile information in the estimation process to reproduce known totals and the distribution of auxiliary variables. We discuss the estimation of the QBIPW probabilities and its variance. Our simulation study has demonstrated that the proposed estimators are robust against model mis-specification and, as a result, help to reduce bias and mean squared error. Finally, we applied the proposed methods to estimate the share of job vacancies aimed at Ukrainian workers in Poland using an integrated set of administrative and survey data about job vacancies.
Release date: 2025-12-23
10. 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

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