Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model

Aalen's nonparametric additive model in which the regression coefficients are assumed to be unspecified functions of time is a flexible alternative to Cox's proportional hazards model when the proportionality assumption is in doubt. In this paper, we incorporate a general linear hypothesis into the estimation of the time‐varying regression coefficients. We combine unrestricted least squares estimators and estimators that are restricted by the linear hypothesis and produce James‐Stein‐type shrinkage estimators of the regression coefficients. We develop the asymptotic joint distribution of such restricted and unrestricted estimators and use this to study the relative performance of the proposed estimators via their integrated asymptotic distributional risks. We conduct Monte Carlo simulations to examine the relative performance of the estimators in terms of their integrated mean square errors. We also compare the performance of the proposed estimators with a recently devised LASSO estimator as well as with ridge‐type estimators both via simulations and data on the survival of primary billiary cirhosis patients.     

On the construction of optimal experimental designs: a penalty approach

Tn optimal experimental design theory there are well-known situations, in which additional constraints are implied to the design set. These constraints destroy in general the simplex structure of the set of feasible points of the design set. Thus the available iteration procedures for the unrestricted case are no longer applicable.

In this paper a penalty approach is suggested which transforms the restricted problem to the unrestricted case and allows the application of well-known algorithms such as the Fedorov-Wynn-type or the projected gradient procedure.     

On sequential closed testing dose groups with a control

Methods for a sequential test of a dose-response effect in pre-clinical studies are investigated. The objective of the test procedure is to compare several dose groups with a zero-dose control. The sequential testing is conducted within a closed family of one-sided tests. The procedures investigated are based on a monotonicity assumption. These closed procedures strongly control the familywise error rate while providing information about the shape of the dose-responce relationship. Performance of sequential testing procedures are compared via a Monte Carlo simulation study. We illustrae the procedures by application to a real data set.     

新型“圆形监狱”——从福柯理论看网络空间的信息监控系统

科学技术极大地提高了生产力,解放了人类,促进了社会的进步和发展。科技的发展在给人类带来福音的同时也带来了一系列负面效应,这在作为当代科技成果集中体现的计算机网络空间中尤为突出。“圆形监狱”一说作为一种以空间来象征权力的理想范例和极致模板首先由边沁提出,而后福柯在《规训与惩罚》中进一步将其描述为全景敞视主义。不管从技术基础、监视模式、空间划分、权力等级等各个方面看,似乎与任何束缚、控制、权力、统治、规训无涉的新型社会空间——网络空间,却在本质上不啻另一种新型的全景敞视“圆形监狱”,实际上是处于一种无形却又无所不在的信息监控网络中,成为了当代资本主义社会的新型统治和渗透手段。因此,传统社会空间中那种明显的、赤裸裸的权力与控制并没有凭空消失,而是以更加全面隐蔽而富有迷惑性的方式渗入网络空间中。这表明,随着现代性的进程,本身作为一种人工产物的网络科技,有可能脱离人的控制而走向未知的自主发展,成为后现代资本社会的新型统治手段而具有负面效应。     

Modal non‐linear regression in the presence of Laplace measurement error

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.     

Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.     

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.