Page 44 - Contributed Paper Session (CPS) - Volume 2

CPS1416 Jungtaek O. et al.

A study on the parameter estimation of the
generalized ratio-type estimator in survey
sampling
Jungtaek OH, Key-Il Shin
Hankuk University of Foreign Studies, Yongin, Rep. of Korea

Abstract
In order to improve the accuracy and the precision of estimation in a sample
survey, a ratio estimator and a regression estimator using auxiliary information
have been widely used. The ratio estimator is simple in its form, convenient to
use, and easy to use for sample weight adjustment. However, the ratio
estimator gives good results only when the variance structure is suitable for
the use. Whereas the regression estimator is relatively complex in form and
difficult to use although the regression estimator gives highly accurate and
robust result for the various distribution types in a survey sampling. In this
study, we propose a generalized ratio-type estimator obtained by
approximating the regression estimator to a ratio-type 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 so the form 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; ratio estimator; Taylor
approximation; Maximum likelihood estimator

1. Introduction
A sample design is carried out using various methods for an optimal
sample survey. Using the optimal sample design can accurately estimate the
parameters of population while reducing costs. Recent decades, the accuracy
and the precision of the estimation have been improved by using
administrative data. Especially in case of business survey, the ratio and the
ratio-type estimator using administrative data are widely used. The ratio and
the ratio-type estimator are known to improve the accuracy and the precision
of parameter estimation using the population parameter values of the auxiliary
variables obtained from administrative data. As is well known, the ratio
estimator is optimized for the ratio model where the variance of the error
satisfies ( ) = , = 1 with the -th auxiliary variable .
2

Therefore, if the error variance of the data does not satisfy this assumption,
the efficiency of the ratio estimator decreases. Hence the ratio estimator
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