Weighting and estimation

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All (638)

All (638) (600 to 610 of 638 results)

601. Unbiased estimation of domain parameters in sampling without replacement Archived
Articles and reports: 12-001-X198400214357
Description:
A finite population of size N is supposed to contain M (unknown) units of a specified category A (say) constituting a domain with mean \mu. A procedure which involves drawing units using simple random sampling without replacement till a preassigned number of members of the domain is reached is proposed. An unbiased estimator of \mu is also derived. This is seen to be superior to the corresponding possibly biased estimator based on a comparable SRSWOR scheme with a fixed number of draws. The proposed scheme is also shown to admit unbiased estimators of M and the domain total T.
Release date: 1984-12-14
602. Evaluation of composite estimation for the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198300214342
Description:
This study considers the suitability of composite estimation techniques for the Canadian Labour Force Survey. The performance of a class of AK composite estimators introduced initially by Gurney and Daly is investigated for several characteristics. While the ordinary composite estimate has a large bias, the AK composite estimate is capable of reducing the bias. Composite estimates having minimum variance and minimum mean square error are compared.
Release date: 1983-12-15
603. The regression estimates or population for sub-provincial areas in Canada Archived
Articles and reports: 12-001-X198300214344
Description:
In order to improve the timeliness, accuracy and consistency of population estimates for different geographic areas, Statistics Canada has developed new methods of estimation for sub-provincial areas (census divisions and census metropolitan areas). Beginning with 1982, two sets of population estimates (regression and component based) will be published yearly, appearing 3-4 months and 12-15 months, respectively, from the reference date.
The regression technique uses family allowance recipients as the main symptomatic indicator and where available, additional indicators - reference population from provincial health insurance files and hydro accounts - to derive population change for the current year. The first set is obtained by adding this change to the second set for the previous year produced by the component method, with births and deaths from vital registers, and estimated migration from Revenue Canada taxation files. The two sets were found to be statistically similar with respect to accuracy, though the first set is more timely, and the second provides more details on the components of population change.
Release date: 1983-12-15
604. The methodology of the Canadian Air Scheduled International Passenger Origin and Destination estimation system Archived
Articles and reports: 12-001-X198300114333
Description:
The Air Scheduled International Passenger Origin and Destination (ASIPOD) estimation system uses the data from two air traffic surveys to produce origin-destination estimates of international passengers. The “assignment technique” is the solution to the problem caused by the non-coverage of non-interlining traffic. The assumptions of the technique are sufficiently questionable to warrant an evaluation of the bias of the estimates. However, major improvements will be made in the new system which will decrease the bias in the estimates. Also, estimates of reliability will be produced. And as a result, knowledge of the strength of the inferences made with respect to air traffic markets from these estimates will be improved in international bilateral air negotiations.
Release date: 1983-06-15
605. Estimating monthly gross flows in labour force participation Archived
Articles and reports: 12-001-X198300114335
Description:
The Canadian Labour Force Survey is a household survey conducted each month for the purpose of producing point-in-time estimates of the number of persons employed, unemployed and not in the labor force. The survey has a rotating panel design in which all individuals in a sampled household location are interviewed each month, for six consecutive months. In the past, little use has been made of this longitudinal structure, although considerable interest has been expressed in the month-to-month gross flows (transitions) amongst the labour force status categories. In this paper we discuss methods being considered by Statistics Canada for the production of gross flow estimates, but from a model-based perspective.
Release date: 1983-06-15
606. Redesign of the Niagara tender fruit objective yield survey Archived
Articles and reports: 12-001-X198300114336
Description:
The peach, sour cherry and the grape objective yield surveys have been carried out annually in the Niagara Peninsula since 1964 in order to forecast the magnitude of change in marketable fruit production from the previous year. Timeliness of the estimates is essential in order to enable the Ontario Tender Fruit Growers Marketing Board (OTFGMB) and the Ontario Grape Growers Marketing Board (OGGMB) to establish the marketing strategies well ahead of the harvest. This paper summarizes the major changes due to the second redesign initiated in 1982. In particular, the sample design, data collection operation and modifications of the estimation procedures are elaborated upon.
Release date: 1983-06-15
607. A timely and accurate potato acreage estimate from Landsat: Results of a demonstration Archived
Articles and reports: 12-001-X198300114337
Description:
This paper describes the procedures used and results of a joint Canada Centre for Remote Sensing (CCRS) and Statistics Canada project to provide a timely potato acreage estimate for New Brunswick, a major potato producing province in Canada. The project has demonstrated that satellite imagery combined with more traditional potato area estimation procedures can lower respondent burden, produce timely crop distribution maps and produce reliable estimates for subregions.
Release date: 1983-06-15
608. Sampling on two occasions with probabilities proportional to size without replacement (PPSWOR) Archived
Articles and reports: 12-001-X198300114340
Description:
A theory of sampling on two occasions with unequal probabilities and without replacement is presented. Fellegi’s (1963) method, which yields the same selection probabilities for a given unit on each occasion, is used to select the units for the rotation sample. The variances of composite estimators of the population total on the second occasion are developed. Numerical results are presented for small sample sizes and efficiency comparisons are made with a competing strategy.
Release date: 1983-06-15
609. Evaluation of small area estimation techniques for the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198200114328
Description:
Estimates from sample surveys are sometimes required for domains whose boundaries do not coincide with those of design strata. Taking the Canadian Labour Force Survey as an example of a survey utilizing a clustered sample design, some alternative small area estimation techniques available in the literature are evaluated empirically including synthetic, domain (simple and post-stratified) and composite estimators which are linear combinations of synthetic and post-stratified domain estimators. A sample dependent estimator which attaches weight to the post-stratified domain estimate depending on the amount of sample in the domain is proposed and its performance is also evaluated.
Release date: 1982-06-15
610. Computerization of complex survey estimates Archived
Articles and reports: 12-001-X198200114331
Description:
Survey data collected by statistical agencies is most likely to be processed through to the tabulation stage by these agencies. The computer programs associated with this processing are also most likely tailored to the particular design and variables used. The statistics computed from such surveys typically range from simple descriptive totals and means to these required for analytic studies such as comparison of domains, regression analysis and contingency tables analysis. This paper describes a computer program which computes these statistics and their associated sampling errors for commonly used sampling designs.
Release date: 1982-06-15

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Analysis (610)

Analysis (610) (60 to 70 of 610 results)

61. 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
62. 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
63. 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
64. 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
65. 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
66. 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
67. 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
68. Optimal linear estimation in two-phase sampling
Articles and reports: 12-001-X202200200011
Description:
Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.
Release date: 2022-12-15
69. Bayesian spatial models for estimating means of sampled and non-sampled small areas
Articles and reports: 12-001-X202200200012
Description:
In many applications, the population means of geographically adjacent small areas exhibit a spatial variation. If available auxiliary variables do not adequately account for the spatial pattern, the residual variation will be included in the random effects. As a result, the independent and identical distribution assumption on random effects of the Fay-Herriot model will fail. Furthermore, limited resources often prevent numerous sub-populations from being included in the sample, resulting in non-sampled small areas. The problem can be exacerbated for predicting means of non-sampled small areas using the above Fay-Herriot model as the predictions will be made based solely on the auxiliary variables. To address such inadequacy, we consider Bayesian spatial random-effect models that can accommodate multiple non-sampled areas. Under mild conditions, we establish the propriety of the posterior distributions for various spatial models for a useful class of improper prior densities on model parameters. The effectiveness of these spatial models is assessed based on simulated and real data. Specifically, we examine predictions of statewide four-person family median incomes based on the 1990 Current Population Survey and the 1980 Census for the United States of America.

Release date: 2022-12-15
70. Market Basket Measure Technical Paper: The other necessities component
Articles and reports: 75F0002M2022006
Description:
This technical paper describes how the cost for "other necessities" is estimated in the 2018-base MBM. It provides a brief overview of the theory and application of techniques for estimating costs of "other necessities" in poverty lines and deconstructs the 2018-base MBM other necessities component to provide insights on how it is constructed. The aim of this paper is to provide a more detailed understanding of how the other necessities component of the MBM is estimated.

Release date: 2022-12-08

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