Location of Multiple Outliers in Two-Way Tables,Using Tetrads

Using residuals to isolate multiple outhers in a two-way table may lead to very poor results. A new diagnostic is proposed: the median of the tetrads associated with a cell. This procedure can efficiently identify multiple outliers in a single step. The use of a half-normal plot provides a good indicator of the actual number of outhers in the table.     

Robust统计在主动声纳分裂波束目标方位走向估计中的应用

主动声纳通常采用分裂波束双通道互谱法进行目标方位估计，但信号处理过程中目标回波脉冲长度往往和信号处理帧周期长度不匹配，或者在整个信号处理帧周期的信噪比不一致，造成瞬时方位估计目标走向算法具有较大的误差，不利于目标参量估计与分类。采用Robust统计对瞬时方位估计数据进行处理，能够有效降低目标方位走向估计的误差。本文通过对Huber估计进行了分析并提出了改进Huber估计，给出了其工程实现算法，实验验证该Robust统计在降低目标方位走向估计误差上具有稳健收敛的性能。     

基于Pena距离的偏Laplace正态数据下位置回归模型的统计诊断

目前医学、社会学、生物等领域都存在尖峰、厚尾且偏斜的数据,针对这类数据,采用偏Laplace正态数据去拟合,得到的结果会更加精确。同时,在统计学中,异常点或强影响点对统计诊断的结果会产生很大的影响,因此对异常点或强影响点的诊断就显得尤为重要。常用的似然距离、Cook距离等研究删除一个(组)点对回归分析与预测值的影响,而Pena距离研究删除样本中各点对某一特定点回归值以及预测值的影响。基于此,在Pena距离下对偏Laplace正态数据下位置回归模型的影响分析进行了研究,利用EM算法对偏Laplace正态分布下的位置回归模型做了统计诊断。得到偏Laplace正态数据下位置回归模型下Pena距离的表达式以及高杠杆异常点的判别方法,并把Pena距离、Cook距离、似然距离进行比较,得到在某些情况下利用Pena距离检测异常点比Cook距离与似然距离更优。模拟与实例研究说明提出的模型与方法具有合理性。     

Robust estimation of mean and variance using environmental data sets with below detection limit observations

Scientists, especially environmental scientists, often encounter trace level concentrations that are typically reported as less than a certain limit of detection, L. Type I left-censored data arises when certain low values lying below L are ignored or unknown as they cannot be measured accurately. In many environmental quality assurance and quality control (QA/QC), and groundwater monitoring applications of the United States Environmental Protection Agency (USEPA), values smaller than L are not required to be reported. However, practitioners still need to obtain reliable estimates of the population mean μ, and the standard deviation (S.D.) σ. The problem gets complex when a small number of high concentrations are observed with a substantial number of concentrations below the detection limit. The high-outlying values contaminate the underlying censored sample, leading to distorted estimates of μ and σ. The USEPA, through the National Exposure Research Laboratory-Las Vegas (NERL-LV), under the Office of Research and Development (ORD), has research interests in developing statistically rigorous robust estimation procedures for contaminated left-censored data sets. Robust estimation procedures based upon a proposed (PROP) influence function are shown to result in reliable estimates of population parameters of mean and S.D. using contaminated left-censored samples. It is also observed that the robust estimates thus obtained with or without the outliers are in close agreement with the corresponding classical estimates after the removal of outliers. Several classical and robust methods for the estimation of μ and σ using left-censored (truncated) data sets with potential outliers have been reviewed and evaluated.     

Estimating the Step‐Change Time of the Location Parameter in Multistage Processes Using MLE

In this paper, maximum likelihood step‐change point estimators of the location parameter, the out‐of‐control sample and the out‐of‐control stage are developed for auto‐correlated multistage processes. To do this, the multistage process and the concept of change detection are first discussed. Then, a time‐series model of the process is presented. Assuming step changes in the location parameter of the process, next, the likelihood functions of different samples before and after receiving out‐of‐control signal from an X‐bar control chart were derived under different conditions. The maximum likelihood estimators were then obtained by maximizing the likelihood functions. Finally, the accuracy and the precision of the proposed estimators are examined through some Monte Carlo simulation experiments. The results show the estimators to be promising. Copyright © 2011 John Wiley & Sons, Ltd.