Correction of the p-Value after Multiple Tests in a Cox Proportional Hazard Model

We consider a situation which is common in epidemiology, in which several transformations of an explanatory variable are tried in a Cox model and the most significant test is retained. The p-value should then be corrected to take account of the multiplicity of tests. Bonferroni method is often too conservative because the tests may be highly positively correlated. We propose an asymptotically exact correction of the p-value. The method uses the fact that the tests are asymptotically normal to compute numerically the distribution of the maximum of several tests. Counting processes theory is used to derive estimators of the correlations between tests. The method is illustrated by a simulation and an analysis of the relation between concentration of aluminum in drinking water and risk of dementia.     

Conditional and predictive probability integral transforms

The conditional probability integral transform, used in goodness-of-fit tests, is compared with its Bayesian counterpart, the predictive probability integral transform, and it is shown that under suitable conditions, in the presence of an adequate group structure, they yield the same transformed random variable, usually uniform on the unit interval.     

沉淀硬化不锈钢PH15—7Mo的组织结构与强化相

本文用定量金相法和膨胀法研究了 PH15～7Mo 钢中,δ铁素体含量,马氏体转变温度和转变量,板条状马氏体和ε马氏体的生成与热处理制度的关系。用射透电子显微镜和x射线相分析法观察和鉴定了析出相的形貌和晶体结构类型。从而阐明该钢的热处理原理和合理使用的温度范围。认为钢材的强化来源于马氏体组织形态和强化相的沉淀硬化效应,强化相为富 Al 相和 Mo 的碳化物。     

Serial correlation and distributions on the shere

Estimation and tests for serial correlation in recation and regression models with normal error have been derive from various points of view; for example: Anderson (1948), Durbi for Watson (1950, 1951, 1971), Theil (1965), Durbin (1970), Haq (1970), Kadiyala (1970), Abrahamse & Louter (1971), Levenbac (1972), Berenblut & Webb (1973), Phillips & Harvey (1974), a Sims (1975). In this paper we derive likelihood functions and most powerful tests for serial correclation in Locationa and regression models with arbitrary but specificed error; the methods extend to include the determination of the likelihood for the parameter of the error distribution.

In Section 2, we survey the modthods that have been used in deriving the various tests and estimates in the literature. In Section 2, we introduce the stataistical model that directly describes the error distribution and we obtain the likelihood function for error correlation and determine locally and specifically kost powerful tests for correlation. In Section 3 we consider the case with normal error derive a normal distribution on the sphere by radial projection. The likelihood function and test are then specialized to the case of normal error in Section 4. The computational procedures for the tests and related power functions are examined in Section 5. Power comparisons for the textile data of Theil and Nagar (1961), the consumption data of Kelin (1950), and the plums and the wheat data of Hildreth & Lu (1960) are presented in Section 6, while the likelihood functions for correlation in these data are given in Section 7.     

On the choice of transformations of the correlation coefficient with or without an outlier

Five transformations of the correlation coefficient, namely, Fisher's z, Nair's u, Sankaran's v, Ruben's y and Samiuddin's t are compared numerically using confidence intervals. Samiuddin's t_s transformation is close to the exact nominal confidence level for a small sample size ≤ 25 from a bivariate normal density. For a sample size > 25 both Samiuddin's t_s and Fisher's z can be used. In the presence of an outlier (on a minor axis), both Fisher's z and Samiuddin's t_s are not affected as long as |p| ≤ 0.3 but are seriously affected when |p&| > 0.3.     

Testable hypotheses in singular fixed linear models

Hypotheses that restrict nonestimable parameters in singular (or overparameterized) fixed linear models are considered nontes table by most aothors and are not allowed by most computer packages. In this article, a different approach is taken and hypotheses are classified as completely testable, partially testable, or nontestable on the basis of the number of degrees of freedom associated with them. The convenience of this approach is illustrated with examples and by developing a related general theory of equivalent hypotheses, reparameterizations, and restrictions. A method of transforming partially testable hypotheses into equivalent completely testable hypotheses is described.     

Best Invariant and Minimax Estimation of Quantiles in Finite Populations

The theoretical literature on quantile and distribution function estimation in infinite populations is very rich, and invariance plays an important role in these studies. This is not the case for the commonly occurring problem of estimation of quantiles in finite populations. The latter is more complicated and interesting because an optimal strategy consists not only of an estimator, but also of a sampling design, and the estimator may depend on the design and on the labels of sampled individuals, whereas in iid sampling, design issues and labels do not exist.We study the estimation of finite population quantiles, with emphasis on estimators that are invariant under the group of monotone transformations of the data, and suitable invariant loss functions. Invariance under the finite group of permutation of the sample is also considered. We discuss nonrandomized and randomized estimators, best invariant and minimax estimators, and sampling strategies relative to different classes. Invariant loss functions and estimators in finite population sampling have a nonparametric flavor, and various natural combinatorial questions and tools arise as a result.     

社会分层结构:机制变革与阶层相互关系

本文讨论了在市场转型过程中,中国社会分层结构中阶层间相互作用关系和结构整合机制的变革。以韦伯关于“依仗命令”和“依仗利益”的两种统治权力的理想类型为概念工具,本文区分了强制性命令权力和交易性权力两种阶层间相互作用关系和结构整合机制,并以中国社会分层结构的转型为基础,分析了上述转变的社会学意义。     

基于生态范式的南京青奥会主题标语翻译

以南京青奥会主题标语的翻译为例，对主题标语提出时的生态环境作出了全新的阐释；同时以生态范式下的多维转换为原则，对主题标语的翻译进行了深入探讨。     

Variance-stabilizing and Confidence-stabilizing Transformations for the Normal Correlation Coefficient with Known Variances

Fosdick and Raftery (2012) recently encountered the problem of inference for a bivariate normal correlation coefficient ρ with known variances. We derive a variance-stabilizing transformation y(ρ) analogous to Fisher’s classical z-transformation for the unknown-variance case. Adjusting y for the sample size n produces an improved “confidence-stabilizing” transformation y_n(ρ) that provides more accurate interval estimates for ρ than the known-variance MLE. Interestingly, the z transformation applied to the unknown-but-equal-variance MLE performs well in the known-variance case for smaller values of |ρ|. Both methods are useful for comparing two or more correlation coefficients in the known-variance case.