A Comparison of Multivariate Ratio Estimators

• Main Authors: HUANG,YAU-YI, 黃耀億
• Other Authors: ESHER HSU
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/19315467521060165397

碩士 === 國立臺北大學 === 統計學系 === 95 === This paper aims to compare the multivariate ratio estimators based upon a Monte Carlo approach. The multivariate ratio estimators explored in this paper are derived from univariate ratio estimators which are summarized from previous studies. Except traditional and Hartley & Ross multivariate ratio estimators proposed by Olkin, no other univariate ratio estimators have been extended to multivariate type. Therefore, in this paper following the Olkin’s concept of expanding univariate ratio estimator to multivariate ratio estimator, the multivariate ratio estimators and their variances are derived and extended from the corresponding univariate ratio estimators which are summarized from previous studied. Using Monte Carlo approach the efficiency of the proposed multivariate ratio estimators are then compared based upon bias, variance, and MSE. The simulation results show that all the other ratio estimators have smaller bias than the traditional ratio estimator for estimating the population total under both of the univariate or multivariate type. The simulation results also find that the bias can be reduced as sample size increased and the variance of ratio estimators are smaller than variance of the mean per unit for estimating population total. That implies that we can reduce the variance of estimator and increase estimation efficiency by increasing sample size or increasing number of groups.