Weighting and estimation
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- Articles and reports: 12-001-X201500214230Description:
This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.
Release date: 2015-12-17 - 2. Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design ArchivedArticles and reports: 12-001-X201500214231Description:
Rotating panels are widely applied by national statistical institutes, for example, to produce official statistics about the labour force. Estimation procedures are generally based on traditional design-based procedures known from classical sampling theory. A major drawback of this class of estimators is that small sample sizes result in large standard errors and that they are not robust for measurement bias. Two examples showing the effects of measurement bias are rotation group bias in rotating panels, and systematic differences in the outcome of a survey due to a major redesign of the underlying process. In this paper we apply a multivariate structural time series model to the Dutch Labour Force Survey to produce model-based figures about the monthly labour force. The model reduces the standard errors of the estimates by taking advantage of sample information collected in previous periods, accounts for rotation group bias and autocorrelation induced by the rotating panel, and models discontinuities due to a survey redesign. Additionally, we discuss the use of correlated auxiliary series in the model to further improve the accuracy of the model estimates. The method is applied by Statistics Netherlands to produce accurate official monthly statistics about the labour force that are consistent over time, despite a redesign of the survey process.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214248Description:
Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.
Release date: 2015-12-17 - 4. Revisions to 2006 to 2011 income data ArchivedSurveys and statistical programs – Documentation: 75F0002M2015003Description:
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 - Surveys and statistical programs – Documentation: 91-528-XDescription:
This manual provides detailed descriptions of the data sources and methods used by Statistics Canada to estimate population. They comprise Postcensal and intercensal population estimates; base population; births and deaths; immigration; emigration; non-permanent residents; interprovincial migration; subprovincial estimates of population; population estimates by age, sex and marital status; and census family estimates. A glossary of principal terms is contained at the end of the manual, followed by the standard notation used.
Until now, literature on the methodological changes for estimates calculations has always been spread throughout various Statistics Canada publications and background papers. This manual provides users of demographic statistics with a comprehensive compilation of the current procedures used by Statistics Canada to prepare population and family estimates.
Release date: 2015-11-17 - Articles and reports: 12-001-X201500114150Description:
An area-level model approach to combining information from several sources is considered in the context of small area estimation. At each small area, several estimates are computed and linked through a system of structural error models. The best linear unbiased predictor of the small area parameter can be computed by the general least squares method. Parameters in the structural error models are estimated using the theory of measurement error models. Estimation of mean squared errors is also discussed. The proposed method is applied to the real problem of labor force surveys in Korea.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114160Description:
Composite estimation is a technique applicable to repeated surveys with controlled overlap between successive surveys. This paper examines the modified regression estimators that incorporate information from previous time periods into estimates for the current time period. The range of modified regression estimators are extended to the situation of business surveys with survey frames that change over time, due to the addition of “births” and the deletion of “deaths”. Since the modified regression estimators can deviate from the generalized regression estimator over time, it is proposed to use a compromise modified regression estimator, a weighted average of the modified regression estimator and the generalised regression estimator. A Monte Carlo simulation study shows that the proposed compromise modified regression estimator leads to significant efficiency gains in both the point-in-time and movement estimates.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114161Description:
A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114172Description:
When a random sample drawn from a complete list frame suffers from unit nonresponse, calibration weighting to population totals can be used to remove nonresponse bias under either an assumed response (selection) or an assumed prediction (outcome) model. Calibration weighting in this way can not only provide double protection against nonresponse bias, it can also decrease variance. By employing a simple trick one can estimate the variance under the assumed prediction model and the mean squared error under the combination of an assumed response model and the probability-sampling mechanism simultaneously. Unfortunately, there is a practical limitation on what response model can be assumed when design weights are calibrated to population totals in a single step. In particular, the choice for the response function cannot always be logistic. That limitation does not hinder calibration weighting when performed in two steps: from the respondent sample to the full sample to remove the response bias and then from the full sample to the population to decrease variance. There are potential efficiency advantages from using the two-step approach as well even when the calibration variables employed in each step is a subset of the calibration variables in the single step. Simultaneous mean-squared-error estimation using linearization is possible, but more complicated than when calibrating in a single step.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29
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Analysis (13) (0 to 10 of 13 results)
- Articles and reports: 12-001-X201500214230Description:
This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.
Release date: 2015-12-17 - 2. Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design ArchivedArticles and reports: 12-001-X201500214231Description:
Rotating panels are widely applied by national statistical institutes, for example, to produce official statistics about the labour force. Estimation procedures are generally based on traditional design-based procedures known from classical sampling theory. A major drawback of this class of estimators is that small sample sizes result in large standard errors and that they are not robust for measurement bias. Two examples showing the effects of measurement bias are rotation group bias in rotating panels, and systematic differences in the outcome of a survey due to a major redesign of the underlying process. In this paper we apply a multivariate structural time series model to the Dutch Labour Force Survey to produce model-based figures about the monthly labour force. The model reduces the standard errors of the estimates by taking advantage of sample information collected in previous periods, accounts for rotation group bias and autocorrelation induced by the rotating panel, and models discontinuities due to a survey redesign. Additionally, we discuss the use of correlated auxiliary series in the model to further improve the accuracy of the model estimates. The method is applied by Statistics Netherlands to produce accurate official monthly statistics about the labour force that are consistent over time, despite a redesign of the survey process.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214248Description:
Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500114150Description:
An area-level model approach to combining information from several sources is considered in the context of small area estimation. At each small area, several estimates are computed and linked through a system of structural error models. The best linear unbiased predictor of the small area parameter can be computed by the general least squares method. Parameters in the structural error models are estimated using the theory of measurement error models. Estimation of mean squared errors is also discussed. The proposed method is applied to the real problem of labor force surveys in Korea.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114160Description:
Composite estimation is a technique applicable to repeated surveys with controlled overlap between successive surveys. This paper examines the modified regression estimators that incorporate information from previous time periods into estimates for the current time period. The range of modified regression estimators are extended to the situation of business surveys with survey frames that change over time, due to the addition of “births” and the deletion of “deaths”. Since the modified regression estimators can deviate from the generalized regression estimator over time, it is proposed to use a compromise modified regression estimator, a weighted average of the modified regression estimator and the generalised regression estimator. A Monte Carlo simulation study shows that the proposed compromise modified regression estimator leads to significant efficiency gains in both the point-in-time and movement estimates.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114161Description:
A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114172Description:
When a random sample drawn from a complete list frame suffers from unit nonresponse, calibration weighting to population totals can be used to remove nonresponse bias under either an assumed response (selection) or an assumed prediction (outcome) model. Calibration weighting in this way can not only provide double protection against nonresponse bias, it can also decrease variance. By employing a simple trick one can estimate the variance under the assumed prediction model and the mean squared error under the combination of an assumed response model and the probability-sampling mechanism simultaneously. Unfortunately, there is a practical limitation on what response model can be assumed when design weights are calibrated to population totals in a single step. In particular, the choice for the response function cannot always be logistic. That limitation does not hinder calibration weighting when performed in two steps: from the respondent sample to the full sample to remove the response bias and then from the full sample to the population to decrease variance. There are potential efficiency advantages from using the two-step approach as well even when the calibration variables employed in each step is a subset of the calibration variables in the single step. Simultaneous mean-squared-error estimation using linearization is possible, but more complicated than when calibrating in a single step.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114192Description:
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as K - composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), AK - composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial Qp defined in terms of the rotation pattern (Qp happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix S defined in terms of the rotation pattern and the roots of the polynomial Qp. In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Release date: 2015-06-29 - 10. A method of determining the winsorization threshold, with an application to domain estimation ArchivedArticles and reports: 12-001-X201500114199Description:
In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.
Release date: 2015-06-29
Reference (5)
Reference (5) ((5 results))
- 1. Revisions to 2006 to 2011 income data ArchivedSurveys and statistical programs – Documentation: 75F0002M2015003Description:
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 - Surveys and statistical programs – Documentation: 91-528-XDescription:
This manual provides detailed descriptions of the data sources and methods used by Statistics Canada to estimate population. They comprise Postcensal and intercensal population estimates; base population; births and deaths; immigration; emigration; non-permanent residents; interprovincial migration; subprovincial estimates of population; population estimates by age, sex and marital status; and census family estimates. A glossary of principal terms is contained at the end of the manual, followed by the standard notation used.
Until now, literature on the methodological changes for estimates calculations has always been spread throughout various Statistics Canada publications and background papers. This manual provides users of demographic statistics with a comprehensive compilation of the current procedures used by Statistics Canada to prepare population and family estimates.
Release date: 2015-11-17 - Surveys and statistical programs – Documentation: 13-605-X201500414166Description:
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 - Surveys and statistical programs – Documentation: 99-002-X2011001Description:
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 - Surveys and statistical programs – Documentation: 99-002-XDescription: 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
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