Asymptoic efficiency of M.L.E. using prior survey in multinomial distributions

Abstract

Incorporating information from a prior survey is generally supposed to decrease the estimation risk of the present survey. This paper aims to show how the risk changes by incorporating the information of a prior survey through watching the first and the second-order terms of the asymptotic expansion of the risk. We recognize that the prior information is of some help for risk reduction when we can acquire samples of a sufficient size for both surveys. Interestingly, when the sample size of the present survey is small, the use of the prior survey can increase the risk. In other words, blending information from both surveys can have a negative effect on the risk. Based on these observations, we give some suggestions on whether or not to use the results of the prior survey and the sample size to use in the surveys for a reliable estimation.

KEYWORDS:

• Kullback–Leibler divergence
• estimation risk
• asymptotic expansion

MSC(2010) Subject Classification:

• Primary 62F10
• Secondary 62F12

Acknowledgment

We appreciate valuable comments of the referees, which enhanced the quality and readability of the paper.