Weighting and estimation

Results

All (638)

All (638) (50 to 60 of 638 results)

51. Application of sampling variance smoothing methods for small area proportion estimation Archived
Articles and reports: 11-522-X202200100005
Description: Sampling variance smoothing is an important topic in small area estimation. In this paper, we propose sampling variance smoothing methods for small area proportion estimation. In particular, we consider the generalized variance function and design effect methods for sampling variance smoothing. We evaluate and compare the smoothed sampling variances and small area estimates based on the smoothed variance estimates through analysis of survey data from Statistics Canada. The results from real data analysis indicate that the proposed sampling variance smoothing methods work very well for small area estimation.
Release date: 2024-03-25
52. Measuring the number of food aid recipients Archived
Articles and reports: 11-522-X202200100013
Description: Respondents to typical household surveys tend to significantly underreport their potential use of food aid distributed by associations. This underreporting is most likely related to the social stigma felt by people experiencing great financial difficulty. As a result, survey estimates of the number of recipients of that aid are much lower than the direct counts from the associations. Those counts tend to overestimate due to double counting. Through its adapted protocol, the Enquête Aide alimentaire (EAA) collected in late 2021 in France at a sample of sites of food aid distribution associations, controls the biases that affect the other sources and determines to what extent this aid is used.
Release date: 2024-03-25
53. Bayesian model assisted design-based estimators of the size, total and mean of a hard-to-reach population from a link-tracing sample with initial cluster sample Archived
Articles and reports: 11-522-X202200100015
Description: We present design-based Horvitz-Thompson and multiplicity estimators of the population size, as well as of the total and mean of a response variable associated with the elements of a hidden population to be used with the link-tracing sampling variant proposed by Félix-Medina and Thompson (2004). Since the computation of the estimators requires to know the inclusion probabilities of the sampled people, but they are unknown, we propose a Bayesian model which allows us to estimate them, and consequently to compute the estimators of the population parameters. The results of a small numeric study indicate that the performance of the proposed estimators is acceptable.
Release date: 2024-03-25
54. Integration of existing data to develop an ethnicity indicator in the LSDDP Archived
Articles and reports: 11-522-X202200100018
Description: The Longitudinal Social Data Development Program (LSDDP) is a social data integration approach aimed at providing longitudinal analytical opportunities without imposing additional burden on respondents. The LSDDP uses a multitude of signals from different data sources for the same individual, which helps to better understand their interactions and track changes over time. This article looks at how the ethnicity status of people in Canada can be estimated at the most detailed disaggregated level possible using the results from a variety of business rules applied to linked data and to the LSDDP denominator. It will then show how improvements were obtained using machine learning methods, such as decision trees and random forest techniques.
Release date: 2024-03-25
55. A method for estimating the effect of classification errors on statistics for two domains
Articles and reports: 12-001-X202300200002
Description: Being able to quantify the accuracy (bias, variance) of published output is crucial in official statistics. Output in official statistics is nearly always divided into subpopulations according to some classification variable, such as mean income by categories of educational level. Such output is also referred to as domain statistics. In the current paper, we limit ourselves to binary classification variables. In practice, misclassifications occur and these contribute to the bias and variance of domain statistics. Existing analytical and numerical methods to estimate this effect have two disadvantages. The first disadvantage is that they require that the misclassification probabilities are known beforehand and the second is that the bias and variance estimates are biased themselves. In the current paper we present a new method, a Gaussian mixture model estimated by an Expectation-Maximisation (EM) algorithm combined with a bootstrap, referred to as the EM bootstrap method. This new method does not require that the misclassification probabilities are known beforehand, although it is more efficient when a small audit sample is used that yields a starting value for the misclassification probabilities in the EM algorithm. We compared the performance of the new method with currently available numerical methods: the bootstrap method and the SIMEX method. Previous research has shown that for non-linear parameters the bootstrap outperforms the analytical expressions. For nearly all conditions tested, the bias and variance estimates that are obtained by the EM bootstrap method are closer to their true values than those obtained by the bootstrap and SIMEX methods. We end this paper by discussing the results and possible future extensions of the method.
Release date: 2024-01-03
56. Small area prediction of general small area parameters for unit-level count data
Articles and reports: 12-001-X202300200003
Description: We investigate small area prediction of general parameters based on two models for unit-level counts. We construct predictors of parameters, such as quartiles, that may be nonlinear functions of the model response variable. We first develop a procedure to construct empirical best predictors and mean square error estimators of general parameters under a unit-level gamma-Poisson model. We then use a sampling importance resampling algorithm to develop predictors for a generalized linear mixed model (GLMM) with a Poisson response distribution. We compare the two models through simulation and an analysis of data from the Iowa Seat-Belt Use Survey.
Release date: 2024-01-03
57. Bayesian small area models under inequality constraints with benchmarking and double shrinkage
Articles and reports: 12-001-X202300200004
Description: We present a novel methodology to benchmark county-level estimates of crop area totals to a preset state total subject to inequality constraints and random variances in the Fay-Herriot model. For planted area of the National Agricultural Statistics Service (NASS), an agency of the United States Department of Agriculture (USDA), it is necessary to incorporate the constraint that the estimated totals, derived from survey and other auxiliary data, are no smaller than administrative planted area totals prerecorded by other USDA agencies except NASS. These administrative totals are treated as fixed and known, and this additional coherence requirement adds to the complexity of benchmarking the county-level estimates. A fully Bayesian analysis of the Fay-Herriot model offers an appealing way to incorporate the inequality and benchmarking constraints, and to quantify the resulting uncertainties, but sampling from the posterior densities involves difficult integration, and reasonable approximations must be made. First, we describe a single-shrinkage model, shrinking the means while the variances are assumed known. Second, we extend this model to accommodate double shrinkage, borrowing strength across means and variances. This extended model has two sources of extra variation, but because we are shrinking both means and variances, it is expected that this second model should perform better in terms of goodness of fit (reliability) and possibly precision. The computations are challenging for both models, which are applied to simulated data sets with properties resembling the Illinois corn crop.
Release date: 2024-01-03
58. Comments by Carl-Erik Särndal on “Jean-Claude Deville’s contributions to survey theory and official statistics”
Articles and reports: 12-001-X202300200012
Description: In recent decades, many different uses of auxiliary information have enriched survey sampling theory and practice. Jean-Claude Deville contributed significantly to this progress. My comments trace some of the steps on the way to one important theory for the use of auxiliary information: Estimation by calibration.
Release date: 2024-01-03
59. Comments by Camelia Goga and Anne Ruiz-Gazen on “Jean-Claude Deville’s contributions to survey theory and official statistics”: Jean-Claude Deville: Mathematics lover, high-flying researcher, and visionary
Articles and reports: 12-001-X202300200013
Description: Jean-Claude Deville is one of the most prominent researcher in survey sampling theory and practice. His research on balanced sampling, indirect sampling and calibration in particular is internationally recognized and widely used in official statistics. He was also a pioneer in the field of functional data analysis. This discussion gives us the opportunity to recognize the immense work he has accomplished, and to pay tribute to him. In the first part of this article, we recall briefly his contribution to the functional principal analysis. We also detail some recent extension of his work at the intersection of the fields of functional data analysis and survey sampling. In the second part of this paper, we present some extension of Jean-Claude’s work in indirect sampling. These extensions are motivated by concrete applications and illustrate Jean-Claude’s influence on our work as researchers.
Release date: 2024-01-03
60. Comments by Françoise Dupont on “Jean-Claude Deville’s contributions to survey theory and official statistics”
Articles and reports: 12-001-X202300200014
Description: Many things have been written about Jean-Claude Deville in tributes from the statistical community (see Tillé, 2022a; Tillé, 2022b; Christine, 2022; Ardilly, 2022; and Matei, 2022) and from the École nationale de la statistique et de l’administration économique (ENSAE) and the Société française de statistique. Pascal Ardilly, David Haziza, Pierre Lavallée and Yves Tillé provide an in-depth look at Jean-Claude Deville’s contributions to survey theory. To pay tribute to him, I would like to discuss Jean-Claude Deville’s contribution to the more day-to-day application of methodology for all the statisticians at the Institut national de la statistique et des études économiques (INSEE) and at the public statistics service. To do this, I will use my work experience, and particularly the four years (1992 to 1996) I spent working with him in the Statistical Methods Unit and the discussions we had thereafter, especially in the 2000s on the rolling census.
Release date: 2024-01-03

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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