A note on Nonparametric Confidence Interval for a Shift Parameter for Cauchy distribution

Abstract

In this article an application of a kernel based nonparametric approach in constructing a large sample nonparametric confidence interval for a shift parameter is considered. The method is illustrated using the Cauchy distribution as a location model. The kernel-based method is found to have a shorter interval for the shift parameter between two Cauchy distributions than the one based on the Mann-Whitney test statistic.

Keywords: Best Asymptotic Normal; Cauchy distribution; Kernel estimates; Mann-Whitney test statistic; Nonparametric confidence interval; Shift parameter.

> East African Journal of Statistics Vol. 1 (1) 2005: pp. 1-8