Research Report SRR03-002

Mean Squared Errors of Ratio Statistics and Bias Corrections

Yoshihiko Maesono

Abstract: Some statistics in common use take a form of a ratio of two statistics such as sample correlation coeiffcient, Pearson's coefficient of variation and so on. In this paper, obtaining an asymptotic representation of the ratio statistic until the third order term, we will discuss asymptotic mean squared errors of the ratio statistics. We will also discuss bias correction of the sample correlation coefficient and the sample coefficient of variation. Mean squared errors of the corrected estimators are also obtained.

AMS Classification: Primary 62E20, Secondary 62G10
Date: 6 February 2003

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