学术讲座预告

Nonparametric Maximum Likelihood Estimation for Distribution Functions

with Ranked Set Samples

主讲人: 张一旻

时  间: 2024/6/25 (Tue.)   9:30

地  点: 数学与统计学院会议室1209

主持人: 陈望学

报告简介

Kvam and Samaniego (1994) derived an estimator that they billed as the nonparametric maximum likelihood estimator (MLE) of the distribution function based on a ranked-set sample. However, we show here that the likelihood used by Kvam and Samaniego (1994) is different from the probability of seeing the observed sample under perfect rankings. By appealing to results on order statistics from a discrete distribution, we write down a likelihood that matches the probability of seeing the observed sample. We maximize this likelihood by using the EM algorithm, and we show that the resulting MLE avoids certain unintuitive behavior exhibited by the Kvam and Samaniego (1994) estimator. We find that the new MLE outperforms both the Kvam and Samaniego (1994) estimator and the unbiased estimator due to Stokes and Sager (1988) in terms of integrated mean squared error under perfect rankings.

嘉宾简介

Dr. Yimin Zhang is a professor of statistics in Department of Mathematics and Statistics at Villanova University. Her research interests include nonparametric statistics, inference on ranked set sampling, statistical modeling and machine learning. Her recent collaborative work spans environmental science, sustainability and transportation.