Weiya Zhang, Ph.D. Candidate : Some Aspects of Statistical Inference on a Normal Mean with Known Coefficient

Posted by , part of the Statistics and Data Science Seminar.

At

March 15, 2006, 2:30 p.m.

In

SEO 512

Abstract

Inference on a normal mean with known CV is intricate since the distribution does not admit of a complete sufficient statistic. Consequently, no umvue exists for the mean. As a result, there have been many attempts to suggest biased estimators which are functions of the sample mean and the sample sd. There is an extensive literature on this fascinating topic. However, the mean parameter is assumed to be positive-valued. If we allow the parameter space to include negative values of the mean as well, the problem of unbiased estimation of the mean in terms of the sample standard deviation becomes intriguing. Starting with the framework of n(>1) i.i.d. observations from a normal population with known CV, we offer (i) an analytical expression for exact unbiased estimator of the mean in terms of the sample sd and the sign function of the sample mean; (ii) an analytical expression for the best linear combination of the estimator in (i) and the sample mean as an unbiased estimator for the mean, along with exact expression for the variance of this linear combination; (iii) a study of asymptotic normality of the linear combination in (ii) as well as its behavior in small samples; (iv) confidence interval for the mean based on a variation of the best linear combination in (ii); (v) comparison of traditional confidence interval for the mean and the one suggested in (iv); (vi) improved fixed width confidence interval for the mean.

There will be a Tea at 2:15pm.