On the Critical Value Behaviour of Multiple Decision Procedures

In this paper we investigate the asymptotic critical value behaviour of certain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing that n hypotheses or parameters of interest are under consideration we investigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence intervals increase when an additional parameter is added to the statistical analysis. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some general theoretic results are derived and applied for various distributions.     

On a fisherian detour of the step-down procedure for manova

The well known step-down procedure for MANOVA given by J. Roy (1958) can be modified by combining the step-down tests using a B-optimal combination method such as Fisher's. The Fisherian detour of the stepwise MANOVA is shown to be asymptotically equivalent to the likelihood ratio test.     

Analysis of incomplete data in experiments with repeated measurements in clinicaltrials using a stochastic model

A stochastic model is proposed to analyze the observation vectors of variable lengths in a long-term clinical trial. Using a Markovian normal density, the likelihood ratio tests for usual hypotheses are derived and asymptotic distributions of the test statistics are obtained. The use of 'step-down' procedure is discussed for the interim analysis and a numerical example is given to illustrate the methodology.     

软起动器在工业和建筑业上的应用

本文以 6ADX型软启动器为例 ,介绍了智能型软启动器的工作原理、功能和特点 ,以及它与传统的起动方式的量化差异及应用方案。     

Nonparametric approaches for comparing three-period,two-treatment,four-sequence crossover designs

The paper describes nonparametric approaches for comparing three-period, two-treatment, four-sequence crossover designs through testing the hypothesis that the treatments are interchangeable. The proposed approaches are based on a model which incorporates, along with the direct treatment effects, self and mixed carryover effects. Related asymptotic results are obtained. Comparisons among the designs are made numerically with respect to type I error rate and power of the tests considering compound symmetry and autoregressive covariance structures of the response variables. Lengths of the confidence intervals of the treatment differences are also used to make comparative study among the designs.     

Comparison to control in logistic regression

We are interested in comparing logistic regressions for several test treatments or populations with a logistic regression for a standard treatment or population. The research was motivated by some real life problems, which are discussed as data examples. We propose a step-down likelihood ratio method for declaring differences between the test treatments or populations and the standard treatment or population. Competitors based on the sequentially rejective Bonferroni Wald statistic, sequentially rejective exact Wald statistic and Reiers?l's statistic are also discussed. It is shown that the proposed method asymptotically controls the probability of type I error. A Monte Carlo simulation shows that the proposed method performs well for relatively small sample sizes, outperforming its competitors.     

Explicit formulas for generalized family-wise error rates and unimprovable step-down multiple testing procedures

Many multiple testing procedures (MTPs) are available today, and their number is growing. Also available are many type I error rates: the family-wise error rate (FWER), the false discovery rate, the proportion of false positives, and others. Most MTPs are designed to control a specific type I error rate, and it is hard to compare different procedures. We approach the problem by studying the exact level at which threshold step-down (TSD) procedures (an important class of MTPs exemplified by the classic Holm procedure) control the generalized FWER   defined as the probability of k$k$ or more false rejections. We find that level explicitly for any TSD procedure and any k$k$. No assumptions are made about the dependency structure of the p$p$-values of the individual tests. We derive from our formula a criterion for unimprovability   of a procedure in the class of TSD procedures controlling the generalized FWER at a given level. In turn, this criterion implies that for each k$k$ the number of such unimprovable procedures is finite and is greater than one if k>1$k>1$. Consequently, in this case the most rejective procedure in the above class does not exist.