Some results on the truncated multivariate t distribution

The use of truncated distributions arises often in a wide variety of scientific problems. In the literature, there are a lot of sampling schemes and proposals developed for various specific truncated distributions. So far, however, the study of the truncated multivariate t (TMVT) distribution is rarely discussed. In this paper, we first present general formulae for computing the first two moments of the TMVT distribution under the double truncation. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for the left and right truncation can be viewed as special cases. We then apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are of uniform distributions. Finally, several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results.     

Added variable plots for linear regression with censored data

In linear regression the structure of the hat matrix plays an important part in regression diagnostics. In this note we investigate the properties of the hat matrix for regression with censored responses in the presence of one or more explanatory variables observed without censoring. The censored points in the scatterplot are renovated to positions had they been observed without censoring in a renovation process based on Buckley-James censored regression estimators. This allows natural links to be established with the structure of ordinary least squares estimators. In particular, we show that the renovated hat matrix may be partitioned in a manner which assists in deciding whether further explanatory variables should be added to the linear model. The added variable plot for regression with censored data is developed as a diagnostic tool for this decision process.     

Variable sampling intervals for multiparameter shewhart charts

This paper considers the problem of using control charts to simultaneously monitor more than one parameter with emphasis on simultaneously monitoring the mean and variance. Fixed sampling interval control charts are modified to use variable sampling intervals depending on what is being observed from the data. Two basic strategies are investigated. One strategy uses separate control charts for each parameter, A second strategy uses a proposed single combined statistic which is sensitive to shifts in both the mean and variance. Each procedure is compared to corresponding fixed interval procedures. It is seen that for both strategies the variable sampling interval approach is substantially more efficient than fixed interval procedures.     

SNP selection for predicting a quantitative trait

Molecular markers combined with powerful statistical tools have made it possible to detect and analyze multiple loci on the genome that are responsible for the phenotypic variation in quantitative traits. The objectives of the study presented in this paper are to identify a subset of single nucleotide polymorphism (SNP) markers that are associated with a particular trait and to construct a model that can best predict the value of the trait given the genotypic information of the SNPs using a three-step strategy. In the first step, a genome-wide association test is performed to screen SNPs that are associated with the quantitative trait of interest. SNPs with p-values of less than 5% are then analyzed in the second step. In the second step, a large number of randomly selected models, each consisting of a fixed number of randomly selected SNPs, are analyzed using the least angle regression method. This step will further remove redundant SNPs due to the complicated association among SNPs. A subset of SNPs that are shown to have a significant effect on the response trait more often than by chance are considered for the third step. In the third step, two alternative methods are considered: the least angle shrinkage and selection operation and sparse partial least squares regression. For both methods, the predictive ability of the fitted model is evaluated by an independent test set. The performance of the proposed method is illustrated by the analysis of a real data set on Canadian Holstein cattle.     

一类非等截面杆的纵向自由振动

研究一类变截面杆，其横截面积呈指数函数变化。经适当变换后，杆的纵向自由振动方程转换为退化的超几何方程，其解可以用Kummer函数来表示。得到了三种简单边界条件下的频率方程和振型函数。频率方程一般是超越方程，需要数值求解其固有频率。在特殊情形下，可以求得各阶固有频率。     

A Transformation Characterizing the Normal Distribution

In this article we propose a new transformation of random variables (RVs) which characterizes the normal distribution. It allows us to transform n i.i.d. normal RVs whose mean and variance are unknown into new n ? 2 i.i.d. new normal variables with zero mean while maintaining the same unknown variance. This belongs to the class of transformations designed to reduce the number of unknown parameters or remove them altogether.

Some historical remarks concerning methods for removing parameters in the normal distribution are given and two possible applications of the new transformation are described.     

基于面板数据的陕西省农村居民消费结构分析

采用个体固定效应变系数模型研究陕西省农村居民消费结构。使用2005--2009年数据，对陕西省农村居民人均消费值进行实证分析。结果表明：在自发人均消费支出中，住房支出位居首位，其次是食品、医疗保健、文教娱乐项目；在人均可支配收入系数之中，低收入者的食品、居住、家庭设备系数值相对中、高收入者要大。比较而言，高收入者在衣着、医疗保健、文化娱乐上的系数值要高；在受上年度人均消费支出影响方面，食品、交通通讯支出影响不显著。     

Estimation for High‐Dimensional Linear Mixed‐Effects Models Using ℓ1‐Penalization

Abstract. We propose an ?₁‐penalized estimation procedure for high‐dimensional linear mixed‐effects models. The models are useful whenever there is a grouping structure among high‐dimensional observations, that is, for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high‐dimensional data set.     

A Note on the Moment Generating Function

A simple proof is given to show that there always exists a neighborhood of zero in which a moment generating function has a power series expansion. Thus, the relation between moments and derivatives of the moment generating function at zero can be obtained without resorting to postcalculus theorems.     

论弗雷格的残篇《论逻辑的普遍性》

弗雷格在其残篇《论逻辑的普遍性》中探讨了思想的普遍性问题,他引入了带有单个字母的辅助语言作为研究普遍性思想的桥梁,普遍性思想的结构分析及其真值条件是弗雷格未完成的内容。普遍性思想的构成部分都是不满足的;普遍性思想的真值条件可以通过理解不同层次概念之间的关系而直接把握,一阶量化理论是理解弗雷格残篇的关键。