Uniform-in-bandwidth kernel estimation for censored data

We present a sharp uniform-in-bandwidth functional limit law for the increments of the Kaplan–Meier empirical process based upon right-censored random data. We apply this result to obtain limit laws for nonparametric kernel estimators of local functionals of lifetime densities, which are uniform with respect to the choices of bandwidth and kernel. These are established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimators are consistent. We provide explicit values for the asymptotic limiting constant for the sup-norm of the estimation random error.     

简论终身体育与高校体育教学

本文通过对终身体育的意义和高校体育现状的分析,就高校体育在如何实现终身体育方面发挥作用提出了自己的论点,以期高校体育教育和终身体育能够有效地接轨。     

Sequential testing with interval censored data ∗

Let X ₁,…,X _n be the lifetimes of n items put on testing at the same time. It is not possible to observe the actual lifetimes. However, it is possible to inspect the items at a finite number of time intervals. At each time of inspection, the number of failures can be recorded. Only these numbers of failures at times of inspections will be available to make decision on the distribution of the lifetimes. Decision can be made at the time of inspection. A “sequential” statistical test is developed to test the mean levels of the lifetimes when the probability distribution is assumed to be exponential. Some numerical results will be presented. The power and the expected time for the decision are compared with those for the idealized situation when each and every actual lifetime is recorded. They are also compared with those for the case when one and only one inspection is allowed to make the decision.     

从苏轼坎坷人生诠释其词的主体情性

苏轼一贯将作家主体情性的自在体现,看成是文艺创作的根本动因和上乘境界.通过对苏轼坎坷人生、豁达性情及其作品的分析,诠释了苏轼词的主体性情与其饱经忧患的人生经历的关系,从而分析出苏轼旷远豪放的词风是与其独特的性情分不开的,这也就是苏词的"风韵"所在.     

考虑客户风险修正的客户终生价值建模

客户终生价值(Customer Lifetime Value,CLV)建模中如何考虑客户风险是目前客户关系管理领域所关注而且有待解决的难题。本文旨在探讨如何通过客户风险修正CLV模型。首先将客户风险划分为包括波动风险、衰退风险、流失风险与信用风险,并提出前三者的度量方法;随后采用改良的贝叶斯网络方法,从条件概率的角度描述了风险之间的关系,同时计算客户风险值;最后,借鉴金融领域对资产进行风险修正的方式,通过贝叶斯网络输出的风险得分,计算客户的Beta风险,对传统的CLV模型中的折现率进行风险修正,得到RCLV模型。本文利用河北省某电信公司的中小企业客户的固定电话数据进行模型仿真和验证,说明所建立模型的合理性和应用价值。     

Influence diagnostics in Birnbaum–Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum–Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8 Galea, M., Leiva, V. and Paula, G. A. 2004. Influence diagnostics in log-Birnbaum–Saunders regression models. J. Appl. Stat., 31: 1049–1064. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]] which are confined to Birnbaum–Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.     

Stochastic EM algorithm for generalized exponential cure rate model and an empirical study

In this paper, we consider two well-known parametric long-term survival models, namely, the Bernoulli cure rate model and the promotion time (or Poisson) cure rate model. Assuming the long-term survival probability to depend on a set of risk factors, the main contribution is in the development of the stochastic expectation maximization (SEM) algorithm to determine the maximum likelihood estimates of the model parameters. We carry out a detailed simulation study to demonstrate the performance of the proposed SEM algorithm. For this purpose, we assume the lifetimes due to each competing cause to follow a two-parameter generalized exponential distribution. We also compare the results obtained from the SEM algorithm with those obtained from the well-known expectation maximization (EM) algorithm. Furthermore, we investigate a simplified estimation procedure for both SEM and EM algorithms that allow the objective function to be maximized to split into simpler functions with lower dimensions with respect to model parameters. Moreover, we present examples where the EM algorithm fails to converge but the SEM algorithm still works. For illustrative purposes, we analyze a breast cancer survival data. Finally, we use a graphical method to assess the goodness-of-fit of the model with generalized exponential lifetimes.     

The modified Fréchet distribution and its properties

The Fréchet distribution is an absolutely continuous model which has wide applicability in extreme value theory. In this paper, we propose a new three-parameter model, so-called the modified Fréchet distribution, to extend the Fréchet distribution. By using the Lambert function, we obtain some properties of the new distribution. We provide a simulation study to illustrate the performance of the maximum likelihood estimates. The flexibility of the introduced distribution is illustrated by means of a real data set. We use some goodness-of-fit statistics to verify the adequacy of the proposed model. We prove empirically that it is appropriate for lifetime applications.     

Test for comparing complete expectations of life of two groups

Abstract

Complete expectation of life of an individual gives an intuitive and interesting perspective on the ageing process and is an important concept in the insurance sector for determination of premium. We propose a new test for testing equality of complete expectations of life of two groups/populations. Power of the new test is calculated through simulations and compared with the power of the tests given by Berger, Boos, and Guess (1988 Berger, R. L., D. D. Boos, and F. M. Guess. 1988. Tests and confidence sets for comparing two mean residual life functions. Biometrics 44 (1):103–15.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Aly (1997 Aly, E. E. A. A. 1997. Nonparametric tests for comparing two mean residual life functions. Lifetime Data Analysis 3 (4):353–66.[Crossref], [PubMed] , [Google Scholar]). It is observed that the proposed test statistic is more powerful than the competing tests for the cases considered in this paper. A real life illustration is included.