A study on the generalized ratio-type estimator based on the multiple regression estimator

Abstract

In order to improve the accuracy and the precision of estimation in a sample survey, the ratio estimator and the regression estimator using auxiliary information have been widely used. The ratio estimator is simple in its form, convenient to use. However, the ratio estimator gives good results only when the variance structure is suitable for the use. On the other hand, even though the regression estimator is relatively complex in form, it gives highly accurate and robust result for the various distribution types. In this study, we propose a generalized ratio-type estimator obtained by approximating a ratio-type estimator to the regression estimator in case with several auxiliary variables. Therefore, the generalized ratio-type estimator has the features of the multiple regression estimator and it has the form of the ratio-type estimator which is simple and easy to use. Through simulation studies, we confirm the theoretical results and the Korea financial statement analysis data are used for real data analysis.

Keywords:

• Sample survey
• weighted least squares estimator
• Taylor approximation
• maximum likelihood estimator

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education(NRF-2014R1A1A2056857).