On Statistical Inference for Scale Parameter with Doubly Censored Data

本論文主旨在研究雙尾設限資料的尺度參數估計式的統計性質與應用。這個估計式適用一般的位置-尺度分配(location-scale distributions)，並且它的變異數有一個容易使用的解析式。應用時，可以先固定樣本數與左尾設限數，然後控制變異數小於預設值，就可以決定右尾設限數。有關不對稱的壽命資料，作者將處理韋伯分配(Weibull distributions)形狀參數的推估問題；這等同於處理極值分配(extreme-value distributions)尺度參數的推估問題。有關對稱的隨機資料，作者將分別導出trimmed mean與Winsorized mean的標準誤的解析式，並以常態分配為例，研究統計量的性質。另外，論文中經常用到順序統計量的期望值、變異數與共變異數，也將提出一般的近似公式。In this article, we will study a robust scale estimator for location-scale distributions with Type II doubly censored data. Its standard error will be derived analytically. Determining censoring numbers under controlling the standard error is studied. For asymmetric distributions, an estimator of the shape parameter of the Weibull distribution will be discussed. Equivalently, we will study the estimator of the scale parameter of Extreme Value distribution. For symmetric distributions, the standard errors of trimmed mean and Winsorized mean will be studied. Some analytical expressions for the means, variances, and covariances of order statistics are derived for our estimators. In the cases of the standard Extreme Value distribution and the standard normal distribution are also discussed