Multiple Linear Regression Model Under Nonnormality

Abstract

We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.     

The Economic Efficiency of Sampling Size: The Case of Beef Trim

The economically optimal sample size in a food safety test balances the marginal costs and marginal benefits of increasing the sample size. We provide a method for selecting the sample size when testing beef trim for Escherichia coli O157:H7 that equates the averted costs of recalls and health damages from contaminated meats sold to consumers with the increased costs of testing while allowing for uncertainty about the underlying prevalence rates of contamination. Using simulations, we show that, in most cases, the optimal sample size is larger than the current sample size of 60 and, in some cases, it exceeds 120. Moreover, lots with a lower prevalence rate have a higher expected damage because contamination is more difficult to detect. Our simulations indicate that these lots have a higher optimal sampling rate.     

Association of educational level and child sex ratio in rural and urban India

Utilizing data from the Census of India, this study compared child sex ratio in rural and urban regions of India and analyzed whether the child sex ratio was associated with mother’s education level. The child sex ratios in the rural and urban regions throughout India were analyzed using the two-sample and paired Student’s t-test. Further, the Chi-square test for trend in binomial proportions was used to assess the association between child sex ratios and mother’s education levels in rural and urban areas. Analysis of the data showed that there was a significant difference between the child sex ratios in rural areas versus urban areas. In addition, the Chi-square test for trend showed that there was a significant association of the child sex ratio and the educational levels of their mothers. This trend occurred in both rural and urban areas.     

车灯反射镜充液拉深液压机的设计

在对车灯反射镜充液拉深工艺数值模拟优化及实验的基础上,研究设计车灯反射镜充液拉深液压机.利用液压提供凸模拉深力、压边力以及凹模容腔压力;通过PLC(可编程控制器)来控制凸模运动、压边力和凹模容腔压力按照规定的曲线实时的变化.结果表明,充液拉深液压机具有体积小、易操作、高精度和高效率等优点.     

Models and methods for pairing data

This paper deals with models and methods for count data derived from observations on pairing phenomena. Pairs formed from “similar” members are excluded. Various models are considered and analyzed. Particular emphasis is on developing methods for testing whether particular pairs are prone to occur more or less often than expected by chance.     

A Cognitive Approach to Direct Practice with the Aging

The recent prominence of cognitive approaches in psychotherapy and more recently in social casework holds considerable promise for direct practice with olderpersons on both an individual and group basis. Several central concepts in cognitive theory are delineated and found to have particular advantages for the aging. First, they deal with conscious concerns and avoid the dangers of affective or regressive approaches in breaking down defenses. Second, they are heavily concerned with questions of meaning and self-concept, issues that are central to the last stage of life, as delineated by Erikson, and the task of achieving ego integrity over despair. Two case illustrations of the application of a cognitive approach in a group context are given.     

THE CHOICE BETWEEN SETS OF REGRESSORS

This paper examines the choice of critical values for testing both non-sequential and nested sequential sets of constraints in the standard linear regression model. Modest increases in (e.g.) t-ratio critical values relative to their one-off values are often sufficient to maintain proper size. A Bayesian decision-theoretic approach, highlighted by the Schwarz (1978) criterion, provides a framework for deriving consistency and asymptotic local power properties of both forms of testing (data mining) algorithms.     

基于浊度检测的洗衣机废水自动回收装置的设计

为回收再利用洗衣机在洗涤过程中所排的废水，设计了洗衣机废水自动回收装置，装置由浊度传感器、液位开关、水用电磁阀、潜水泵、水箱等构成。该装置可自动识别废水污浊程度，从而决定是否回收储存起来。经简易处理的回收废水类似于q-水，可用于马桶及地面的冲洗，这对于水资源的节约利用、绿色住宅建筑设施设计具有一定的参考意义，同时也具有一定的经济效益。     

Conditional interval estimation of the mean following rejection of a two sided test

The effect of rejecting a two-sided preliminary test of significance for the mean of a normal distribution upon subsequent interval estimation of the mean is examined. For the case where the variance is known, conditional confidence intervals may be shorter than unconditional intervals, in contrast to the one-sided preliminary test case examined by Meeks and D’Agostino (1983, The American Statistician, 7, 134-136) . For the case where the variance is unknown and must be estimated by the sample variance, it is shown that customary intervals do not offer uniformly greater or lesser coverage than the nominal level.     

对散手运动员疲劳产生机制及其恢复手段的探讨

进入21世纪以来,散手比赛中运动员技术水平和竞技能力日益提高,其运动特点决定了要对运动员进行高强度、高密度的训练。这就难免在运动和训练过程中出现疲劳,必将对系统训练和运动寿命等造成影响,怎样恢复便成为了一个重要的问题,本文针对散手运动员疲劳产生的原因,提出了疲劳恢复的方法和手段。