Two multivariate generalized beta families

A multivariate generalized beta distribution is introduced that extends the univariate generalized beta distribution and includes many multivariate distributions, such as the multivariate beta of the first and second kind, the generalized gamma, and the Burr and Dirichlet distributions as special and limiting cases. These interrelationships can be illustrated using a distributional family tree. The corresponding marginal distributions are univariate generalized beta distributions and their special cases. Selected expressions for the moments are reported, and an application to the joint distribution of income and wealth is presented. A simple transformation of the multivariate generalized beta distribution leads to what will be referred to as a multivariate exponential generalized beta distribution, which includes a multivariate form of the logistics and Burr distributions as special cases.     

Relationship between the weighted distributions and some inequality measures

In this paper, we study the relationships between the weighted distributions and the parent distributions in the context of Lorenz curve, Lorenz ordering and inequality measures. These relationships depend on the nature of the weight functions and give rise to interesting connections. The properties of weighted distributions for general weight functions are also investigated. It is shown how to derive and to determine characterizations related to Lorenz curve and other inequality measures for the cases weight functions are increasing or decreasing. Some of the results are applied for special cases of the weighted distributions. We represent the reliability measures of weighted distributions by the inequality measures to obtain some results. Length-biased and equilibrium distributions have been discussed as weighted distributions in the reliability context by concentration curves. We also review and extend the problem of stochastic orderings and aging classes under weighting. Finally, the relationships between the weighted distribution and transformations are discussed.     

Notes on two sample tests for partially correlated (paired) data

We provide several methods to compare two Gaussian distributed means in the two sample location problems under the assumption of partially dependent observations. Simulation studies indicate that our test procedure is frequently more powerful than other methods depending on the ratio of the unpaired data and the strength and direction of the correlation between the two variables. The tests used in our comparative study are illustrated with an example based on data from a small gynecological study.     

Moment-Implied Densities: Properties and Applications

Suppose one uses a parametric density function based on the first four (conditional) moments to model risk. There are quite a few densities to choose from and depending on which is selected, one implicitly assumes very different tail behavior and very different feasible skewness/kurtosis combinations. Surprisingly, there is no systematic analysis of the tradeoff one faces. It is the purpose of the article to address this. We focus on the tail behavior and the range of skewness and kurtosis as these are key for common applications such as risk management.     

Analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable. We develop the essential methodology for estimating the model parameters via maximum likelihood method. The general form of the maximum likelihood estimator is obtained in color closed form. Adjusted treatment effects and adjusted covariate effects are given, too. We also provide the asymptotic distribution of the proposed estimators. A simulation study and a real world application are also performed to illustrate and evaluate the proposed methodology.     

Variable selection for multivariate generalized linear models

Generalized linear models (GLMs) are widely studied to deal with complex response variables. For the analysis of categorical dependent variables with more than two response categories, multivariate GLMs are presented to build the relationship between this polytomous response and a set of regressors. Traditional variable selection approaches have been proposed for the multivariate GLM with a canonical link function when the number of parameters is fixed in the literature. However, in many model selection problems, the number of parameters may be large and grow with the sample size. In this paper, we present a new selection criterion to the model with a diverging number of parameters. Under suitable conditions, the criterion is shown to be model selection consistent. A simulation study and a real data analysis are conducted to support theoretical findings.     

Variable selection in the high-dimensional continuous generalized linear model with current status data

In survival studies, current status data are frequently encountered when some individuals in a study are not successively observed. This paper considers the problem of simultaneous variable selection and parameter estimation in the high-dimensional continuous generalized linear model with current status data. We apply the penalized likelihood procedure with the smoothly clipped absolute deviation penalty to select significant variables and estimate the corresponding regression coefficients. With a proper choice of tuning parameters, the resulting estimator is shown to be a root n/p_n-consistent estimator under some mild conditions. In addition, we show that the resulting estimator has the same asymptotic distribution as the estimator obtained when the true model is known. The finite sample behavior of the proposed estimator is evaluated through simulation studies and a real example.     

A graphical evaluation of logistic ridge estimator in mixture experiments

In comparison to other experimental studies, multicollinearity appears frequently in mixture experiments, a special study area of response surface methodology, due to the constraints on the components composing the mixture. In the analysis of mixture experiments by using a special generalized linear model, logistic regression model, multicollinearity causes precision problems in the maximum-likelihood logistic regression estimate. Therefore, effects due to multicollinearity can be reduced to a certain extent by using alternative approaches. One of these approaches is to use biased estimators for the estimation of the coefficients. In this paper, we suggest the use of logistic ridge regression (RR) estimator in the cases where there is multicollinearity during the analysis of mixture experiments using logistic regression. Also, for the selection of the biasing parameter, we use fraction of design space plots for evaluating the effect of the logistic RR estimator with respect to the scaled mean squared error of prediction. The suggested graphical approaches are illustrated on the tumor incidence data set.     

算子方程A~nX(A~*)~n=B的解

利用算子矩阵分块技巧,在算子A值域闭的情况下研究了算子方程AnX(A*)n=B的解及正解的存在性,最后给出了正解的一般结构.