Weighting and estimation
Results
All (9)
All (9) ((9 results))
- 1. Unequal probability inverse sampling ArchivedArticles and reports: 12-001-X201600214660Description:
In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214663Description:
We present theoretical evidence that efforts during data collection to balance the survey response with respect to selected auxiliary variables will improve the chances for low nonresponse bias in the estimates that are ultimately produced by calibrated weighting. One of our results shows that the variance of the bias – measured here as the deviation of the calibration estimator from the (unrealized) full-sample unbiased estimator – decreases linearly as a function of the response imbalance that we assume measured and controlled continuously over the data collection period. An attractive prospect is thus a lower risk of bias if one can manage the data collection to get low imbalance. The theoretical results are validated in a simulation study with real data from an Estonian household survey.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214664Description:
This paper draws statistical inference for finite population mean based on judgment post stratified (JPS) samples. The JPS sample first selects a simple random sample and then stratifies the selected units into H judgment classes based on their relative positions (ranks) in a small set of size H. This leads to a sample with random sample sizes in judgment classes. Ranking process can be performed either using auxiliary variables or visual inspection to identify the ranks of the measured observations. The paper develops unbiased estimator and constructs confidence interval for population mean. Since judgment ranks are random variables, by conditioning on the measured observations we construct Rao-Blackwellized estimators for the population mean. The paper shows that Rao-Blackwellized estimators perform better than usual JPS estimators. The proposed estimators are applied to 2012 United States Department of Agriculture Census Data.
Release date: 2016-12-20 - 4. Tests for evaluating nonresponse bias in surveys ArchivedArticles and reports: 12-001-X201600214677Description:
How do we tell whether weighting adjustments reduce nonresponse bias? If a variable is measured for everyone in the selected sample, then the design weights can be used to calculate an approximately unbiased estimate of the population mean or total for that variable. A second estimate of the population mean or total can be calculated using the survey respondents only, with weights that have been adjusted for nonresponse. If the two estimates disagree, then there is evidence that the weight adjustments may not have removed the nonresponse bias for that variable. In this paper we develop the theoretical properties of linearization and jackknife variance estimators for evaluating the bias of an estimated population mean or total by comparing estimates calculated from overlapping subsets of the same data with different sets of weights, when poststratification or inverse propensity weighting is used for the nonresponse adjustments to the weights. We provide sufficient conditions on the population, sample, and response mechanism for the variance estimators to be consistent, and demonstrate their small-sample properties through a simulation study.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600114540Description:
In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.
Release date: 2016-06-22 - Articles and reports: 12-001-X201600114543Description:
The regression estimator is extensively used in practice because it can improve the reliability of the estimated parameters of interest such as means or totals. It uses control totals of variables known at the population level that are included in the regression set up. In this paper, we investigate the properties of the regression estimator that uses control totals estimated from the sample, as well as those known at the population level. This estimator is compared to the regression estimators that strictly use the known totals both theoretically and via a simulation study.
Release date: 2016-06-22 - 7. Register-based sampling for household panels ArchivedArticles and reports: 12-001-X201600114544Description:
In the Netherlands, statistical information about income and wealth is based on two large scale household panels that are completely derived from administrative data. A problem with using households as sampling units in the sample design of panels is the instability of these units over time. Changes in the household composition affect the inclusion probabilities required for design-based and model-assisted inference procedures. Such problems are circumvented in the two aforementioned household panels by sampling persons, who are followed over time. At each period the household members of these sampled persons are included in the sample. This is equivalent to sampling with probabilities proportional to household size where households can be selected more than once but with a maximum equal to the number of household members. In this paper properties of this sample design are described and contrasted with the Generalized Weight Share method for indirect sampling (Lavallée 1995, 2007). Methods are illustrated with an application to the Dutch Regional Income Survey.
Release date: 2016-06-22 - Articles and reports: 82-003-X201600414489Description:
Using accelerometry data for children and youth aged 3 to 17 from the Canadian Health Measures Survey, the probability of adherence to physical activity guidelines is estimated using a conditional probability, given the number of active and inactive days distributed as a Betabinomial.
Release date: 2016-04-20 - Articles and reports: 11-522-X201700014737Description:
Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data. In particular, the actual type I error rates of tests of hypotheses based on standard tests can be much bigger than the nominal level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests (Rao, Scott and Skinner 1998) that involve the estimated covariance matrices of parameter estimates. The bootstrap method of Rao and Wu (1983) is often applied at Statistics Canada to estimate the covariance matrices, using the data file containing columns of bootstrap weights. Standard statistical packages often permit the use of survey weighted test statistics and it is attractive to approximate their distributions under the null hypothesis by their bootstrap analogues computed from the bootstrap weights supplied in the data file. Beaumont and Bocci (2009) applied this bootstrap method to testing hypotheses on regression parameters under a linear regression model, using weighted F statistics. In this paper, we present a unified approach to the above method by constructing bootstrap approximations to weighted likelihood ratio statistics and weighted quasi-score statistics. We report the results of a simulation study on testing independence in a two way table of categorical survey data. We studied the relative performance of the proposed method to alternative methods, including Rao-Scott corrected chi-squared statistic for categorical survey data.
Release date: 2016-03-24
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Analysis (9)
Analysis (9) ((9 results))
- 1. Unequal probability inverse sampling ArchivedArticles and reports: 12-001-X201600214660Description:
In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214663Description:
We present theoretical evidence that efforts during data collection to balance the survey response with respect to selected auxiliary variables will improve the chances for low nonresponse bias in the estimates that are ultimately produced by calibrated weighting. One of our results shows that the variance of the bias – measured here as the deviation of the calibration estimator from the (unrealized) full-sample unbiased estimator – decreases linearly as a function of the response imbalance that we assume measured and controlled continuously over the data collection period. An attractive prospect is thus a lower risk of bias if one can manage the data collection to get low imbalance. The theoretical results are validated in a simulation study with real data from an Estonian household survey.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214664Description:
This paper draws statistical inference for finite population mean based on judgment post stratified (JPS) samples. The JPS sample first selects a simple random sample and then stratifies the selected units into H judgment classes based on their relative positions (ranks) in a small set of size H. This leads to a sample with random sample sizes in judgment classes. Ranking process can be performed either using auxiliary variables or visual inspection to identify the ranks of the measured observations. The paper develops unbiased estimator and constructs confidence interval for population mean. Since judgment ranks are random variables, by conditioning on the measured observations we construct Rao-Blackwellized estimators for the population mean. The paper shows that Rao-Blackwellized estimators perform better than usual JPS estimators. The proposed estimators are applied to 2012 United States Department of Agriculture Census Data.
Release date: 2016-12-20 - 4. Tests for evaluating nonresponse bias in surveys ArchivedArticles and reports: 12-001-X201600214677Description:
How do we tell whether weighting adjustments reduce nonresponse bias? If a variable is measured for everyone in the selected sample, then the design weights can be used to calculate an approximately unbiased estimate of the population mean or total for that variable. A second estimate of the population mean or total can be calculated using the survey respondents only, with weights that have been adjusted for nonresponse. If the two estimates disagree, then there is evidence that the weight adjustments may not have removed the nonresponse bias for that variable. In this paper we develop the theoretical properties of linearization and jackknife variance estimators for evaluating the bias of an estimated population mean or total by comparing estimates calculated from overlapping subsets of the same data with different sets of weights, when poststratification or inverse propensity weighting is used for the nonresponse adjustments to the weights. We provide sufficient conditions on the population, sample, and response mechanism for the variance estimators to be consistent, and demonstrate their small-sample properties through a simulation study.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600114540Description:
In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.
Release date: 2016-06-22 - Articles and reports: 12-001-X201600114543Description:
The regression estimator is extensively used in practice because it can improve the reliability of the estimated parameters of interest such as means or totals. It uses control totals of variables known at the population level that are included in the regression set up. In this paper, we investigate the properties of the regression estimator that uses control totals estimated from the sample, as well as those known at the population level. This estimator is compared to the regression estimators that strictly use the known totals both theoretically and via a simulation study.
Release date: 2016-06-22 - 7. Register-based sampling for household panels ArchivedArticles and reports: 12-001-X201600114544Description:
In the Netherlands, statistical information about income and wealth is based on two large scale household panels that are completely derived from administrative data. A problem with using households as sampling units in the sample design of panels is the instability of these units over time. Changes in the household composition affect the inclusion probabilities required for design-based and model-assisted inference procedures. Such problems are circumvented in the two aforementioned household panels by sampling persons, who are followed over time. At each period the household members of these sampled persons are included in the sample. This is equivalent to sampling with probabilities proportional to household size where households can be selected more than once but with a maximum equal to the number of household members. In this paper properties of this sample design are described and contrasted with the Generalized Weight Share method for indirect sampling (Lavallée 1995, 2007). Methods are illustrated with an application to the Dutch Regional Income Survey.
Release date: 2016-06-22 - Articles and reports: 82-003-X201600414489Description:
Using accelerometry data for children and youth aged 3 to 17 from the Canadian Health Measures Survey, the probability of adherence to physical activity guidelines is estimated using a conditional probability, given the number of active and inactive days distributed as a Betabinomial.
Release date: 2016-04-20 - Articles and reports: 11-522-X201700014737Description:
Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data. In particular, the actual type I error rates of tests of hypotheses based on standard tests can be much bigger than the nominal level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests (Rao, Scott and Skinner 1998) that involve the estimated covariance matrices of parameter estimates. The bootstrap method of Rao and Wu (1983) is often applied at Statistics Canada to estimate the covariance matrices, using the data file containing columns of bootstrap weights. Standard statistical packages often permit the use of survey weighted test statistics and it is attractive to approximate their distributions under the null hypothesis by their bootstrap analogues computed from the bootstrap weights supplied in the data file. Beaumont and Bocci (2009) applied this bootstrap method to testing hypotheses on regression parameters under a linear regression model, using weighted F statistics. In this paper, we present a unified approach to the above method by constructing bootstrap approximations to weighted likelihood ratio statistics and weighted quasi-score statistics. We report the results of a simulation study on testing independence in a two way table of categorical survey data. We studied the relative performance of the proposed method to alternative methods, including Rao-Scott corrected chi-squared statistic for categorical survey data.
Release date: 2016-03-24
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