<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We consider longitudinal data and the problem of prediction of subpopulation (domain) characteristics that can be written as a linear combination of the variable of interest, including cases of small or zero sample sizes in the domain and time period of interest. We consider the empirical version of the predictor proposed by Royall (1976) showing that it is a generalization of the empirical version of the predictor presented by Henderson (1950). We propose a parametric bootstrap MSE estimator of the predictor. We prove its asymptotic unbiasedness and derive the order of its bias. Considerations are supported by Monte Carlo simulation analyses to compare its accuracy (not only the bias) with other MSE estimators, including jackknife and weighted jackknife MSE estimators that we adapt for the considered predictor.</p>
</abstract>

We consider longitudinal data and the problem of prediction of subpopulation (domain) characteristics that can be written as a linear combination of the variable of interest, including cases of small or zero sample sizes in the domain and time period of interest. We consider the empirical version of the predictor proposed by Royall (1976) showing that it is a generalization of the empirical version of the predictor presented by Henderson (1950). We propose a parametric bootstrap MSE estimator of the predictor. We prove its asymptotic unbiasedness and derive the order of its bias. Considerations are supported by Monte Carlo simulation analyses to compare its accuracy (not only the bias) with other MSE estimators, including jackknife and weighted jackknife MSE estimators that we adapt for the considered predictor.

On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems

Department of Statistics, Econometrics and Mathematics

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider longitudinal data and the problem of prediction of subpopulation (domain) characteristics that can be written as a linear combination of the...

On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems

Published Online: Jun 15, 2020

Page range: 435 - 458

Received: Apr 01, 2019

Accepted: Jan 01, 2020

DOI: https://doi.org/10.2478/jos-2020-0022

Keywords
Empirical best linear unbiased predictor, model approach in survey sampling, parametric bootstrap, properties of MSE estimators, small area estimation

© 2020 Tomasz Żądło, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems

Published Online: Jun 15, 2020

Page range: 435 - 458

Received: Apr 01, 2019

Accepted: Jan 01, 2020

DOI: https://doi.org/10.2478/jos-2020-0022

KeywordsEmpirical best linear unbiased predictor, model approach in survey sampling, parametric bootstrap, properties of MSE estimators, small area estimation

© 2020 Tomasz Żądło, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Empirical best linear unbiased predictor, model approach in survey sampling, parametric bootstrap, properties of MSE estimators, small area estimation