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• 1. Linearization variance estimators for survey data Archived

  Articles and reports: 12-001-X20040016991

  Description:

  In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.

  Release date: 2004-07-14

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• 2. Prediction of finite population totals based on the sample distribution Archived

  Articles and reports: 12-001-X20040016996

  Description:

  This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.

  Release date: 2004-07-14

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• 1. Linearization variance estimators for survey data Archived

  Articles and reports: 12-001-X20040016991

  Description:

  In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.

  Release date: 2004-07-14

  ---

• 2. Prediction of finite population totals based on the sample distribution Archived

  Articles and reports: 12-001-X20040016996

  Description:

  This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.

  Release date: 2004-07-14

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