無母數分配中心點已知條件下之對稱型分位數及截斷變異數

Abstract

With the assumption of known the center of the distribution of a random variable, we study the estimation of population quantile and a trimmed population variance. For estimating the population quantile function for the symmetric location model, we show that the sample symmetric quantile is asymptotically more efficient in the sense of smaller asymptotic variance and then shorter confidence interval than those by the ordinary sample quantile. For estimation of the trimmed variance, we compare the sample trimmed variance constructed by ordinary quantiles and the symmetric type sample trimmed variance. Although these two estimators are asymptotically equivalent in distribution, however, a small sample Monte Carlo comparison shows that the latter one is relatively more efficient than the former one in terms of mean squares errors.