Assaad Houssein I, Choudhary Pankaj K
Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA.
Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083-0688, USA.
J Nonparametr Stat. 2013;25(2):499-521. doi: 10.1080/10485252.2013.772178. Epub 2013 Mar 15.
The -statistics form an important class of estimators in nonparametric statistics. Its members include trimmed means and sample quantiles and functions thereof. This article is devoted to theory and applications of -statistics for repeated measurements data, wherein the measurements on the same subject are dependent and the measurements from different subjects are independent. This article has three main goals: (a) Show that the -statistics are asymptotically normal for repeated measurements data. (b) Present three statistical applications of this result, namely, location estimation using trimmed means, quantile estimation and construction of tolerance intervals. (c) Obtain a Bahadur representation for sample quantiles. These results are generalizations of similar results for independently and identically distributed data. The practical usefulness of these results is illustrated by analyzing a real data set involving measurement of systolic blood pressure. The properties of the proposed point and interval estimators are examined via simulation.
U统计量是非参数统计中一类重要的估计量。其成员包括截尾均值、样本分位数及其函数。本文致力于重复测量数据的U统计量的理论与应用，其中同一受试者的测量值是相关的，而不同受试者的测量值是独立的。本文有三个主要目标：(a) 证明对于重复测量数据，U统计量是渐近正态的。(b) 给出这一结果的三个统计应用，即使用截尾均值进行位置估计、分位数估计和容忍区间的构建。(c) 获得样本分位数的Bahadur表示。这些结果是独立同分布数据类似结果的推广。通过分析一个涉及收缩压测量的真实数据集来说明这些结果的实际用途。通过模拟检验了所提出的点估计和区间估计的性质。
