Additional variables and adjusted estimates with arbitrary known variance-covariance structure

When additional variables are fitted in a linear model under arbitrary known variance-covariance struture, the extra sum of squares due to fitting the new variables and adjusted parameter estimates can be computed in an efficient manner without actually explicity fitting the entire augmented model. When the additional variables are specific dummy variables, downdating formulae are readily obtained, thus generatina methods which are well known for the linear model with variance-covariance structure σ²I. Two different methods to downdate a linear model are presented.     

不同模覆盖系的模倒数之和

构造性证明了当Z的不同模覆盖系最小模为2,3与4时,其模倒数之和可任意接近于1或2,并提出两个未解决问题.     

关于积分区间可加性定理的证明

指出数学分析现用教材中定积分性质定理６证明中的错误，并给出正确的证     

The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables

Abstract

An expression for the exact cumulative distribution function of a ratio of quadratic forms in noncentral normal variable is derived in terms of infinite series of top order invariant polynomials.     

Simulating the average run length for cusum schemes using variance reduction techniques

Some variance reduction techniques utilizing the total hazard are developed to estimate the average run lengths of the cumulative sum charts through simulation when the process follows a general probability distribution. Particularly, we propose the hazard estimator and the cycle estimator. Simulation results are shown for the exponential case and these estimators are compared with the raw simulation estimator. Applicability to multivariate CUSUM schemes is briefly discussed in the conclusion.     

金额/比率陈述方式和调节匹配对消费者购买意愿的影响

研究引入调节匹配这个源于心理学的概念,探讨两种不同目标导向——求成与避败的消费者面对两种不同的信息陈述方式——金额与比率时对购买意愿的影响。结果表明：信息陈述方式与消费者目标导向产生匹配,才能对消费者态度及其购买意愿产生积极的正面影响;消费者动机存在干扰效果,尤其在消费者属于高动机的情况下,原本对促销信息陈述没有匹配的消费者转变为匹配,且消费者态度明显提升。     

自然数方幂和中的Stirling数研究

给出了自然数方幂和的包含Ｓｔｉｒｌｉｎｇ数的几种精确表示式，得到了Ｓｔｉｒｌｉｎｇ数的一些新的性质和Ｂｅｒｎｏｕｌｉ数的计数式．     

等幂和的一种构造方法

构造高度等幂和是数论中一个困难问题，利用多重和的指标变换给出由低度等幂和构造高度等幂和的方法，并且给出构造10度等幂和的例子。     

Exponential progressive step-stress life-testing with link function based on Box–Cox transformation

In order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this article, we discuss a k-stage step-stress accelerated life-test with M-stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box–Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique is developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out.     

An almost sure central limit theorem for self-normalized partial sums of weakly dependent random variables

Abstract

We give here an almost sure central limit theorem for self-normalized partial sums of a strictly stationary φ-mixing sequences which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Our result substantially extend a result on the almost sure central limit theorem previously obtained by Huang and Pang (2010).