Statistics and Data Science Seminar
Weiya Zhang, Ph.D. Candidate
MSCS, UIC
Some Aspects of Statistical Inference on a Normal Mean with Known Coefficient
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.
Wednesday March 15, 2006 at 2:30 PM in SEO 512