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- 1. A computer algebra for sample survey theory ArchivedArticles and reports: 12-001-X19970013100Description:
A system of procedures that can be used to automate complicated algebraic calculations frequently encountered in sample survey theory is introduced. It is shown that three basic techniques in sampling theory depend on the repeated application of rules that give rise to partitions: the computation of expected values under any unistage sampling design, the determination of unbiased or consistent estimators under these designs and the calculation of Taylor series expansions. The methodology is illustrated here through applications to moment calculations of the sample mean, the ratio estimator and the regression estimator under the special case of simply random sampling without replacement. The innovation presented here is that calculations can now be performed instantaneously on a computer without error and without reliance on existing formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae presently exist. The computer code developed to implement this methodology is available via anonymous ftp at fisher.stats.uwo.ca.
Release date: 1997-08-18 - Articles and reports: 12-001-X19970013102Description:
The selection of auxiliary variables is considered for regression estimation in finite populations under a simple random sampling design. This problem is a basic one for model-based and model-assisted survey sampling approaches and is of practical importance when the number of variables available is large. An approach is developed in which a mean squared error estimator is minimised. This approach is compared to alternative approaches using a fixed set of auxiliary variables, a conventional significance test criterion, a condition number reduction approach and a ridge regression approach. The proposed approach is found to perform well in terms of efficiency. It is noted that the variable selection approach affects the properties of standard variance estimators and thus leads to a problem of variance estimation.
Release date: 1997-08-18 - Articles and reports: 12-001-X19970013106Description:
The standard error estimation method used for sample data in the U.S. Decennial Census from 1970 through 1990 yielded irregular results. For example, the method gave different standard error estimates for the "yes" and "no" response for the same binomial variable, when both standard error estimates should have been the same. If most respondents answered a binomial variable one way and a few answered the other way, the standard error estimate was much higher for the response with the most respondents. In addition, when 100 percent of respondents answered a question the same way, the standard error of this estimate was not zero, but was still quite high. Reporting average design effects which were weighted by the number of respondents that reported particular characteristics magnified the problem. An alternative to the random groups standard error estimate used in the U.S. census is suggested here.
Release date: 1997-08-18 - 4. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30 - Articles and reports: 12-001-X19960022979Description:
This paper empirically compares three estimation methods - regression, restricted regression, and principal person - used in a household survey of consumer expenditures. The three methods are applied to post-stratification which is important in many household surveys to adjust for under-coverage of the target population. Post-stratum population counts are typically available from an external census for numbers of persons but not for numbers of households. If household estimates are needed, a single weight must be assigned to each household while using the person counts for post-stratification. This is easily accomplished with regression estimators of totals or means by using person counts in each household's auxiliary data. Restricted regression estimation refines the weights by controlling extremes and can produce estimators with lower variance than Horvitz-Thompson estimators while still adhering to the population controls. The regression methods also allow controls to be used for both person-level counts and quantitative auxiliaries. With the principal person method, persons are classified into post-strata and person weights are ratio adjusted to achieve population control totals. This leads to each person in a household potentially having a different weight. The weight associated with the "principal person" is then selected as the household weight. We will compare estimated means from the three methods and their estimated standard errors for a number of expenditures from the Consumer Expenditure survey sponsored by the U.S. Bureau of Labor Statistics.
Release date: 1997-01-30 - 6. A transformation method for finite population sampling calibrated with empirical likelihood ArchivedArticles and reports: 12-001-X19960022980Description:
In this paper, we study a confidence interval estimation method for a finite population average when some auxiliairy information is available. As demonstrated by Royall and Cumberland in a series of empirical studies, naive use of existing methods to construct confidence intervals for population averages may result in very poor conditional coverage probabilities, conditional on the sample mean of the covariate. When this happens, we propose to transform the data to improve the precision of the normal approximation. The transformed data are then used to make inference on the original population average, and the auxiliary information is incorporated into the inference directly, or by calibration with empirical likelihood. Our approach is design-based. We apply our approach to six real populations and find that when transformation is needed, our approach performs well compared to the usual regression method.
Release date: 1997-01-30 - 7. Stability measures for variance component estimators under a stratified multistage design ArchivedArticles and reports: 12-001-X19960022982Description:
In work with sample surveys, we often use estimators of the variance components associated with sampling within and between primary sample units. For these applications, it can be important to have some indication of whether the variance component estimators are stable, i.e., have relatively low variance. This paper discusses several data-based measures of the stability of design-based variance component estimators and related quantities. The development emphasizes methods that can be applied to surveys with moderate or large numbers of strata and small numbers of primary sample units per stratum. We direct principal attention toward the design variance of a within-PSU variance estimator, and two related degrees-of-freedom terms. A simulation-based method allows one to assess whether an observed stability measure is consistent with standard assumptions regarding variance estimator stability. We also develop two sets of stability measures for design-based estimators of between-PSU variance components and the ratio of the overall variance to the within-PSU variance. The proposed methods are applied to interview and examination data from the U.S. Third National Health and Nutrition Examination Survey (NHANES III). These results indicate that the true stability properties may vary substantially across variables. In addition, for some variables, within-PSU variance estimators appear to be considerably less stable than one would anticipate from a simple count of secondary units within each stratum.
Release date: 1997-01-30
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- 1. A computer algebra for sample survey theory ArchivedArticles and reports: 12-001-X19970013100Description:
A system of procedures that can be used to automate complicated algebraic calculations frequently encountered in sample survey theory is introduced. It is shown that three basic techniques in sampling theory depend on the repeated application of rules that give rise to partitions: the computation of expected values under any unistage sampling design, the determination of unbiased or consistent estimators under these designs and the calculation of Taylor series expansions. The methodology is illustrated here through applications to moment calculations of the sample mean, the ratio estimator and the regression estimator under the special case of simply random sampling without replacement. The innovation presented here is that calculations can now be performed instantaneously on a computer without error and without reliance on existing formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae which may be long and involved. One other immediate benefit of this is that calculations can be performed where no formulae presently exist. The computer code developed to implement this methodology is available via anonymous ftp at fisher.stats.uwo.ca.
Release date: 1997-08-18 - Articles and reports: 12-001-X19970013102Description:
The selection of auxiliary variables is considered for regression estimation in finite populations under a simple random sampling design. This problem is a basic one for model-based and model-assisted survey sampling approaches and is of practical importance when the number of variables available is large. An approach is developed in which a mean squared error estimator is minimised. This approach is compared to alternative approaches using a fixed set of auxiliary variables, a conventional significance test criterion, a condition number reduction approach and a ridge regression approach. The proposed approach is found to perform well in terms of efficiency. It is noted that the variable selection approach affects the properties of standard variance estimators and thus leads to a problem of variance estimation.
Release date: 1997-08-18 - Articles and reports: 12-001-X19970013106Description:
The standard error estimation method used for sample data in the U.S. Decennial Census from 1970 through 1990 yielded irregular results. For example, the method gave different standard error estimates for the "yes" and "no" response for the same binomial variable, when both standard error estimates should have been the same. If most respondents answered a binomial variable one way and a few answered the other way, the standard error estimate was much higher for the response with the most respondents. In addition, when 100 percent of respondents answered a question the same way, the standard error of this estimate was not zero, but was still quite high. Reporting average design effects which were weighted by the number of respondents that reported particular characteristics magnified the problem. An alternative to the random groups standard error estimate used in the U.S. census is suggested here.
Release date: 1997-08-18 - 4. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30 - Articles and reports: 12-001-X19960022979Description:
This paper empirically compares three estimation methods - regression, restricted regression, and principal person - used in a household survey of consumer expenditures. The three methods are applied to post-stratification which is important in many household surveys to adjust for under-coverage of the target population. Post-stratum population counts are typically available from an external census for numbers of persons but not for numbers of households. If household estimates are needed, a single weight must be assigned to each household while using the person counts for post-stratification. This is easily accomplished with regression estimators of totals or means by using person counts in each household's auxiliary data. Restricted regression estimation refines the weights by controlling extremes and can produce estimators with lower variance than Horvitz-Thompson estimators while still adhering to the population controls. The regression methods also allow controls to be used for both person-level counts and quantitative auxiliaries. With the principal person method, persons are classified into post-strata and person weights are ratio adjusted to achieve population control totals. This leads to each person in a household potentially having a different weight. The weight associated with the "principal person" is then selected as the household weight. We will compare estimated means from the three methods and their estimated standard errors for a number of expenditures from the Consumer Expenditure survey sponsored by the U.S. Bureau of Labor Statistics.
Release date: 1997-01-30 - 6. A transformation method for finite population sampling calibrated with empirical likelihood ArchivedArticles and reports: 12-001-X19960022980Description:
In this paper, we study a confidence interval estimation method for a finite population average when some auxiliairy information is available. As demonstrated by Royall and Cumberland in a series of empirical studies, naive use of existing methods to construct confidence intervals for population averages may result in very poor conditional coverage probabilities, conditional on the sample mean of the covariate. When this happens, we propose to transform the data to improve the precision of the normal approximation. The transformed data are then used to make inference on the original population average, and the auxiliary information is incorporated into the inference directly, or by calibration with empirical likelihood. Our approach is design-based. We apply our approach to six real populations and find that when transformation is needed, our approach performs well compared to the usual regression method.
Release date: 1997-01-30 - 7. Stability measures for variance component estimators under a stratified multistage design ArchivedArticles and reports: 12-001-X19960022982Description:
In work with sample surveys, we often use estimators of the variance components associated with sampling within and between primary sample units. For these applications, it can be important to have some indication of whether the variance component estimators are stable, i.e., have relatively low variance. This paper discusses several data-based measures of the stability of design-based variance component estimators and related quantities. The development emphasizes methods that can be applied to surveys with moderate or large numbers of strata and small numbers of primary sample units per stratum. We direct principal attention toward the design variance of a within-PSU variance estimator, and two related degrees-of-freedom terms. A simulation-based method allows one to assess whether an observed stability measure is consistent with standard assumptions regarding variance estimator stability. We also develop two sets of stability measures for design-based estimators of between-PSU variance components and the ratio of the overall variance to the within-PSU variance. The proposed methods are applied to interview and examination data from the U.S. Third National Health and Nutrition Examination Survey (NHANES III). These results indicate that the true stability properties may vary substantially across variables. In addition, for some variables, within-PSU variance estimators appear to be considerably less stable than one would anticipate from a simple count of secondary units within each stratum.
Release date: 1997-01-30
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