Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices

We propose a new test procedure for testing linear hypothesis on the mean vectors of normal populations with unequal covariance matrices when the dimensionality, p exceeds the sample size N  , i.e. p/N→c<∞$p/N\to c<\infty$. Our procedure is based on the Dempster trace criterion and is shown to be consistent in high dimensions.     

The Asymptotic Approximation of EPMC for Linear Discriminant Rules Using a Moore-Penrose Inverse Matrix in High Dimension

We consider the discriminant rule in a high-dimensional setting, i.e., when the number of feature variables p is comparable to or larger than the number of observations N. The discriminant rule must be modified in order to cope with singular sample covariance matrix in high-dimension. One way to do so is by considering the Moor-Penrose inverse matrix. Recently, Srivastava (2006 Srivastava , M. S. ( 2006 ). Minimum distance classification rules for high dimensional data . J. Multivariate Anal. 97 : 2057 – 2070 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed maximum likelihood ratio rule by using Moor-Penrose inverse matrix of sample covariance matrix. In this article, we consider the linear discriminant rule by using Moor-Penrose inverse matrix of sample covariance matrix (LDRMP). With the discriminant rule, the expected probability of misclassification (EPMC) is commonly used as measure of the classification accuracy. We investigate properties of EPMC for LDRMP in high-dimension as well as the one of the maximum likelihood rule given by Srivastava (2006 Srivastava , M. S. ( 2006 ). Minimum distance classification rules for high dimensional data . J. Multivariate Anal. 97 : 2057 – 2070 .[Crossref], [Web of Science ®] , [Google Scholar]). From our asymptotic results, we show that the classification accuracy of LDRMP depends on new distance. Additionally, our asymptotic result is verified by using the Monte Carlo simulation.     

Simultaneous Tests for Independence Among Components of Random Vector by Step-Down Multiple Comparison Procedure

In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ² distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down multiple comparison procedure based on the closed testing procedure proposed by Marcus et al. (1976 Marcus , R. , Peritz , E. , Gabriel , K. R. ( 1976 ). On closed testing procedures with special reference to ordered analysis of variance . Biometrika 63 : 655 – 660 .[Crossref], [Web of Science ®] , [Google Scholar]). Finally, we perform Monte Carlo simulations and present numerical results.     

A Monte Carlo comparison of Jarque–Bera type tests and Henze–Zirkler test of multivariate normality

In the paper, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Tests proposed by Mardia and Srivastava, and the combined tests based on skewness and kurtosis defined by Jarque and Bera have been taken into account. In the Monte Carlo simulations, for each combination of p = 2, 3, 4, 5 number of traits and n = 10(5)50(10)100 sample sizes 10,000 runs have been done to calculate empirical Type I errors of tests under consideration, and empirical power against different alternative distributions. Simulation results have been compared to the Henze–Zirkler’s test. It should be stressed that no test yet proposed is uniformly better than all the others in every combination of conditions examined.     

Ross' measure of risk aversion and portfolio selection

This article shows that if Ross' definition of riskier is replaced by a more traditional definition, such as a mean-preserving spread or second-degree stochastic dominance, then the application of Ross's stronger measure of risk aversion to the portfolio problem may no longer produce the desired result. It is also shown that the stronger measure may not perform satisfactorily when applied to exponential utility functions.The authors are grateful to John Pratt for his helpful comments.     

Robust Bayesian estimation of a two-parameter exponential distribution under generalized Type-I progressive hybrid censoring

A generalized Type-I progressive hybrid censoring scheme was proposed recently to overcome the limitations of the progressive hybrid censoring scheme. In this article, we provide a robust Bayesian method to estimate the unknown parameters of the two-parameter exponential distribution of a generalized Type-I progressive hybrid censored sample. For each parameter, we derive the marginal posterior density functions and the corresponding Bayesian estimators under the squared error loss function. To assess the proposed method, Monte Carlo simulations are performed using a real dataset.     

Bayesian inference on extreme value distribution using upper record values

In this paper we address estimation and prediction problems for extreme value distributions under the assumption that the only available data are the record values. We provide some properties and pivotal quantities, and derive unbiased estimators for the location and rate parameters based on these properties and pivotal quantities. In addition, we discuss mean-squared errors of the proposed estimators and exact confidence intervals for the rate parameter. In Bayesian inference, we develop objective Bayesian analysis by deriving non informative priors such as the Jeffrey, reference, and probability matching priors for the location and rate parameters. We examine the validity of the proposed methods through Monte Carlo simulations for various record values of size and present a real data set for illustration purposes.     

Prevalence of Sexual Dysfunction and Associated Risk Factors in Middle-Aged and Elderly Korean Men in Primary Care

Although several studies have individually investigated the risk factors for erectile dysfunction (ED), premature ejaculation (PE), and late-onset hypogonadism (LOH), few studies have considered ED, PE, and LOH as categories of sexual dysfunction (SD) within the same population. We therefore aimed to investigate the prevalence of SD and its associated risk factors among men in primary care. Study participants were enrolled by 18 family physicians from 15 hospital-based family practices in Korea between August 2010 and May 2011. Participants answered a questionnaire regarding their demographic characteristics and lifestyle factors as well as the Korean versions of the Androgen Deficiency in the Aging Male, the International Index of Erectile Function, and the Premature Ejaculation Diagnostic Tool questionnaires. SD prevalence was 64.9% among study participants who were ≥ 40 years of age. ED prevalence was 43.7%, PE prevalence was 38.6%, and LOH prevalence was 16.8%. SD prevalence was significantly associated with increased age, overweight, hypertension, diabetes, and depression. These findings highlight the importance of screening questions for SD in primary care, especially among older male patients with the identified risk factors.