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.     

组建科研团队提升地方高校科技实力

目的/意义习近平总书记在哲学社会科学工作座谈会上发表的重要讲话推动了哲学社会科学进入到新的发展阶段,哲学社会科学创新团队的发展是繁荣哲学社会科学、推动社会进步发展的重要力量,充分发挥哲学社会科学创新团队在社会经济建设中的积极作用,对于实现创新型国家战略具有重要意义。设计/方法在对哲学社会科学创新团队特征进行分析的基础上,界定了其内在合作成效的内涵,之后运用指示优先级的程式化(Priority-Pointing Procedure)方法,对影响社会科学类创新团队内在合作的因素进行初步识别与集成,进而基于DEMATEL方法对影响因素的相关性予以深入分析,探索其内在机理。结论/发现对哲学社会科学创新团队内在合作成效影响因素机理进行分析,得出影响哲学社会科学创新团队内在合作成效的最终原因因素为学科交叉融合、沟通与冲突管理,而个体满意度及未来发展、成果分配及应用是最终结果因素,并提出哲学社会科学创新团队内在合作成效提升的途径。     

Assessing the Concept of the ‘Insecure‐Other’ Category in the Cassidy–Marvin Scheme: Changes Between 4 and 6 Years in the English and Romanian Adoptee Study

We set out to explore the meaning of the attachment categories in the Cassidy/Marvin strange situation procedure, as employed in the home, using data from a longitudinal study of children adopted into UK families up to the age of 42 months from Romanian institutions, and of adopted children without the experience of institutional care––both groups being assessed at 4 and 6 years of age. Inter‐rater reliability was found to be good. Security (meaning the use of the parent as a secure base and no negative behavior on reunion) was the modal categorical rating in both the institution‐reared and comparison groups, but the category of anomalous non‐normative behavior (meaning a lack of any ordered attachment behavior as covered by the standard ratings), previously labeled ‘insecure‐other’, was more common in the institution‐reared children. Because this was unassociated with the usual manifestations of insecurity (such as avoidance or resistance) and because it was largely evident in interactions with the stranger, it is concluded that the adjective ‘insecure’ was not appropriate. Although this ‘insecure‐other’ category was associated with disinhibited attachment as reported by parents (meaning a lack of differentiation among adults, a willingness to go off with strangers and a lack of checking back with parents in anxiety‐provoking situations), it did not prove to be a good index of disinhibited attachment because changes over time in the ‘insecure‐other’ category were not associated with changes in the rate of disinhibited attachment. Also, whereas the rate of ‘insecure‐other’ fell markedly in the institution‐reared group between 4 and 6 years of age, it rose in the comparison group, raising queries over its meaning.     

Controlling the familywise error rate with plug-in estimator for the proportion of true null hypotheses

Summary.  Estimation of the number or proportion of true null hypotheses in multiple-testing problems has become an interesting area of research. The first important work in this field was performed by Schweder and Spjøtvoll. Among others, they proposed to use plug-in estimates for the proportion of true null hypotheses in multiple-test procedures to improve the power. We investigate the problem of controlling the familywise error rate FWER when such estimators are used as plug-in estimators in single-step or step-down multiple-test procedures. First we investigate the case of independent p -values under the null hypotheses and show that a suitable choice of plug-in estimates leads to control of FWER in single-step procedures. We also investigate the power and study the asymptotic behaviour of the number of false rejections. Although step-down procedures are more difficult to handle we briefly consider a possible solution to this problem. Anyhow, plug-in step-down procedures are not recommended here. For dependent p -values we derive a condition for asymptotic control of FWER and provide some simulations with respect to FWER and power for various models and hypotheses.     

Multiple Comparison Procedures: The Practical Solution

A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.     

Bivariate exponential-type distributions with linear regression

Let Xbe a bivariate exponential-type random vector (BIDLIKAR, PATIL (1968)), than it is proved:

1. If P(X ≥0) = 1 is valid, then Xhas linear regression to both directions if and only if Xpossesses a symmetric Γ-distribution.

2. Xpossesses linear regression to both directions with constant regression coefficients (independent of the parameter vector ? of the exponential-type distribution (BIDLIKAR, PATIL (1968)) if and only if Xis normal distributed.     

Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings.     

Bonferroni-type Plug-in Procedure Controlling Generalized Familywise Error Rate

Consider the multiple hypotheses testing problem controlling the generalized familywise error rate k-FWER, the probability of at least k false rejections. We propose a plug-in procedure based on the estimation of the number of true null hypotheses. Under the independence assumption of the p-values corresponding to the true null hypotheses, we first introduce the least favorable configuration (LFC) of k-FWER for Bonferroni-type plug-in procedure, then we construct a plug-in k-FWER-controlled procedure based on LFC. For dependent p-values, we establish the asymptotic k-FWER control under some mild conditions. Simulation studies suggest great improvement over generalized Bonferroni test and generalized Holm test.     

Inferences on regression coefficients in a regression model under heteroscedasticity and robustness with respect to departure from normality

In this paper we consider a simple linear regression model under heteroscedasticity and nonnormality. A statistical test for testing the regression coefficient is then derived by assuming normality for the random disturbances and by applying Welch's method. Some Monte Carlo studies are generated for assessing robustness of this test. By combining Tiku's robust procedure with the new test, a robust but more powerful test is developed.     

Mixed Graphical Model Selection Using Holm's Procedure

The problem of selecting a graphical model is considered as a performing simultaneously multiple tests. The control of the overall Type I error on the selected graph is done using the so famous Holm's procedure. We prove that when we use a consistent edge exclusion test the selected graph is asymptotically equal to the true graph with probability at least equal to a fixed level 1 ? α. This method is then used for the selection of mixed concentration graph models by performing the χ²-edge exclusion test. We also apply the method to two classical examples and to simulated data. We compare the overall error of the selected model with the one obtained using the stepwise method. We establish that the control is better when we use the Holm's procedure.