Distribution of the two‐sample t‐test statistic following blinded sample size re‐estimation

We consider the blinded sample size re‐estimation based on the simple one‐sample variance estimator at an interim analysis. We characterize the exact distribution of the standard two‐sample t‐test statistic at the final analysis. We describe a simulation algorithm for the evaluation of the probability of rejecting the null hypothesis at given treatment effect. We compare the blinded sample size re‐estimation method with two unblinded methods with respect to the empirical type I error, the empirical power, and the empirical distribution of the standard deviation estimator and final sample size. We characterize the type I error inflation across the range of standardized non‐inferiority margin for non‐inferiority trials, and derive the adjusted significance level to ensure type I error control for given sample size of the internal pilot study. We show that the adjusted significance level increases as the sample size of the internal pilot study increases. Copyright © 2016 John Wiley & Sons, Ltd.     

基于灰色系统的小型精密机床热误差模型

为减少热误差对数控机床加工精度的影响,文章利用灰色系统研究热误差建模。初步分析机床热源后,应用灰 色关联度分析结合模糊分类方法优化得到13组关键温度测点,结合小型精密五轴机床处于实际加工状态时的实验数 据,应用GM(I,N)灰色结构进行建模。将实际数据与拟合数据进行对比分析,结果表明此灰色系统模型具有计算方法 成熟、鲁棒性强的特点,适用于机床热误差研究。     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

Bayesian estimation and influence diagnostics of generalized partially linear mixed-effects models for longitudinal data

This paper develops a Bayesian approach to obtain the joint estimates of unknown parameters, nonparametric functions and random effects in generalized partially linear mixed models (GPLMMs), and presents three case deletion influence measures to identify influential observations based on the φ-divergence, Cook's posterior mean distance and Cook's posterior mode distance of parameters. Fisher's iterative scoring algorithm is developed to evaluate the posterior modes of parameters in GPLMMs. The first-order approximation to Cook's posterior mode distance is presented. The computationally feasible formulae for the φ-divergence diagnostic and Cook's posterior mean distance are given. Several simulation studies and an example are presented to illustrate our proposed methodologies.     

Methods to assess measurement error in questionnaires of sedentary behavior

Sedentary behavior has already been associated with mortality, cardiovascular disease, and cancer. Questionnaires are an affordable tool for measuring sedentary behavior in large epidemiological studies. Here, we introduce and evaluate two statistical methods for quantifying measurement error in questionnaires. Accurate estimates are needed for assessing questionnaire quality. The two methods would be applied to validation studies that measure a sedentary behavior by both questionnaire and accelerometer on multiple days. The first method fits a reduced model by assuming the accelerometer is without error, while the second method fits a more complete model that allows both measures to have error. Because accelerometers tend to be highly accurate, we show that ignoring the accelerometer's measurement error, can result in more accurate estimates of measurement error in some scenarios. In this article, we derive asymptotic approximations for the mean-squared error of the estimated parameters from both methods, evaluate their dependence on study design and behavior characteristics, and offer an R package so investigators can make an informed choice between the two methods. We demonstrate the difference between the two methods in a recent validation study comparing previous day recalls to an accelerometer-based ActivPal.     

儒家的尚"中"与道家的崇"大"——儒道和谐观的差异与融合

"和谐"作为中国传统文化的一个核心范畴,是一个多层次、立体的概念,儒家的尚"中"思想及由此而发展起来的"中和"观念与道家的崇"大"思想及由此而来的"大和"观念是构成这一理论的两大基石,前者为"和谐"观念的形成提供了秩序平衡与个体节中,后者则带来了本体追求与辩证观念.在《易传》与《中庸》中二者达到融合.     

论"中"

“中”的思想在中国历史渊源流长,成为中华民族人文精神的核心,也是中国哲学的精髓。《周易》倡导“中和”精神,儒家践行中庸之道,佛家崇尚以中观法,道家提倡守中致道,都从不同角度深刻地阐发了“中”的思想。万物皆有中,中是一切存在的根本属性,“中律”是宇宙万物运行的根本法则,中和是创新的灵魂。     

A non-parametric statistic for testing conditional heteroscedasticity for unobserved component models

When prediction intervals are constructed using unobserved component models (UCM), problems can arise due to the possible existence of components that may or may not be conditionally heteroscedastic. Accurate coverage depends on correctly identifying the source of the heteroscedasticity. Different proposals for testing heteroscedasticity have been applied to UCM; however, in most cases, these procedures are unable to identify the heteroscedastic component correctly. The main issue is that test statistics are affected by the presence of serial correlation, causing the distribution of the statistic under conditional homoscedasticity to remain unknown. We propose a nonparametric statistic for testing heteroscedasticity based on the well-known Wilcoxon''s rank statistic. We study the asymptotic validation of the statistic and examine bootstrap procedures for approximating its finite sample distribution. Simulation results show an improvement in the size of the homoscedasticity tests and a power that is clearly comparable with the best alternative in the literature. We also apply the test on real inflation data. Looking for the presence of a conditionally heteroscedastic effect on the error terms, we arrive at conclusions that almost all cases are different than those given by the alternative test statistics presented in the literature.     

Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

A smoothed bootstrap method is presented for the purpose of bandwidth selection in nonparametric hazard rate estimation for iid data. In this context, two new bootstrap bandwidth selectors are established based on the exact expression of the bootstrap version of the mean integrated squared error of some approximations of the kernel hazard rate estimator. This is very useful since Monte Carlo approximation is no longer needed for the implementation of the two bootstrap selectors. A simulation study is carried out in order to show the empirical performance of the new bootstrap bandwidths and to compare them with other existing selectors. The methods are illustrated by applying them to a diabetes data set.