Methods for high-dimensional multivariate and multi-group repeated measures data under non-normality

Asymptotic tests for multivariate repeated measures are derived under non-normality and unspecified dependence structure. Notwithstanding their broader scope of application, the methods are particularly useful when a random vector of large number of repeated measurements are collected from each subject but the number of subjects per treatment group is limited. In some experimental situations, replicating the experiment large number of times could be expensive or infeasible. Although taking large number of repeated measurements could be relatively cheaper, due to within subject dependence the number of parameters involved could get large pretty quickly. Under mild conditions on the persistence of the dependence, we have derived asymptotic multivariate tests for the three testing problems in repeated measures analysis. The simulation results provide evidence in favour of the accuracy of the approximations to the null distributions.     

A note on information theoretic measures

An axiomatic characterization of an information theoretic quantity is given using only two axioms. In particular, this quantity contain PEARSON'S chi-square statistic and some other useful measures     

A Bayesian approach for analysing longitudinal nominal outcomes using random coefficients transitional generalized logit model: an application to the labour force survey data

A random-effects transition model is proposed to model the economic activity status of household members. This model is introduced to take into account two kinds of correlations; one due to the longitudinal nature of the study, which will be considered using a transition parameter, and the other due to the existing correlation between responses of members of the same household which is taken into account by introducing random coefficients into the model. The results are presented based on the homogeneous (all parameters are not changed by time) and non-homogeneous Markov models with random coefficients. A Bayesian approach via the Gibbs sampling is used to perform parameter estimation. Results of using random-effects transition model are compared, using deviance information criterion, with those of three other models which exclude random effects and/or transition effects. It is shown that the full model gains more precision due to the consideration of all aspects of the process which generated the data. To illustrate the utility of the proposed model, a longitudinal data set which is extracted from the Iranian Labour Force Survey is analysed to explore the simultaneous effect of some covariates on the current economic activity as a nominal response. Also, some sensitivity analyses are performed to assess the robustness of the posterior estimation of the transition parameters to the perturbations of the prior parameters.     

An Appraisal of Methods for the Analysis of Longitudinal Ordinal Response Data with Random Dropout Using a Nonhomogeneous Markov Model

There are many methods for analyzing longitudinal ordinal response data with random dropout. These include maximum likelihood (ML), weighted estimating equations (WEEs), and multiple imputations (MI). In this article, using a Markov model where the effect of previous response on the current response is investigated as an ordinal variable, the likelihood is partitioned to simplify the use of existing software. Simulated data, generated to present a three-period longitudinal study with random dropout, are used to compare performance of ML, WEE, and MI methods in terms of standardized bias and coverage probabilities. These estimation methods are applied to a real medical data set.     

An L-statistic approach to a test of exponentiality against IFR alternatives

In this note we consider the problem of testing exponentiality against IFR alternatives. A measure of deviation from exponentiality is developed and a test statistic constructed on the basis of this measure. It is shown that the test statistic is an L-statistic. The asymptotic as well as the exact distribution of the test statistic is obtained and the test is shown to be consistent.     

A Versatile One-Dimensional Distribution Plot: The BLiP Plot

A versatile graphical tool, the BLiP plot, was developed for displaying one-dimensional data. The basic building blocks are boxes, lines, and points. Like many standard one-dimensional distribution plots, the BLiP plot is capable of displaying individual data values in points or lines and grouped information in lines or boxes. In addition, the BLiP plot includes many new features such as variable-width plots and several choices of point patterns. The main advantage of the BLiP plot is that it provides users with basic graphical elements in a friendly and flexible environment so that users can, according to their needs, construct anything from a simple, standard plot to a complex, customized plot to best present their data.     

On the moments of record values

In this paper some general relations for expectations of functions of record values are established. It is seen that these relations may be used to obtain recurrence relations for moments of record values. Bounds on expectations of record values with numerical computations are presented. Applications to the characterizations of the generalizeed exponential distribution are also given.     

Estimation of P(Y < X) for Weibull Distribution Under Progressive Type-II Censoring

Based on progressively Type II censored samples, we consider the estimation of R = P(Y < X) when X and Y are two independent Weibull distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator, approximate maximum likelihood estimator, and Bayes estimator of R are obtained. Based on the asymptotic distribution of R, the confidence interval of R are obtained. Two bootstrap confidence intervals are also proposed. Analysis of a real data set is given for illustrative purposes. Monte Carlo simulations are also performed to compare the different proposed methods.     

车辆路径问题的三阶段求解方法研究

针对由车辆路径问题规模的增大带采求解空间组合爆炸这一难点,从缩减解答空间入手,以节省求解时空为突破口,综合运用知识工程、模糊聚类分析、状态空间搜索理论和运筹学整数规划理论,提出一种求解车辆路径问题的三阶段求解方法.第一阶段分析物流配送过程的主要影响因素,根据相关因素对客户进行初步划分,然后采用模糊聚类分析方法将各配送区域中的客户进行细分;第二阶段采用带控制策略的深度优先搜索算法生成备选的车辆路径方案集合;第三阶段建立整数规划求解模型,并根据邻域规则将求得的解映射为实际问题中的行车方案.最后运用算例验证上述方法的有效性.