Generalized empirical likelihood inference in partial linear regression model for longitudinal data

In this paper, empirical likelihood inference for longitudinal data within the framework of partial linear regression models are investigated. The proposed procedures take into consideration the correlation within groups without involving direct estimation of nuisance parameters in the correlation matrix. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence intervals. A nonparametric version of Wilk's theorem for the limiting distribution of the empirical likelihood ratio is derived. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. The finite sample behaviour of the proposed method is evaluated with simulation and illustrated with an AIDS clinical trial data set.     

Estimation of odds ratios under order restrictions

A new method for estimating a set of odds ratios under an order restriction based on estimating equations is proposed. The method is applied to those of the conditional maximum likelihood estimators and the Mantel-Haenszel estimators. The estimators derived from the conditional likelihood estimating equations are shown to maximize the conditional likelihoods. It is also seen that the restricted estimators converge almost surely to the respective odds ratios when the respective sample sizes become large regularly. The restricted estimators are compared with the unrestricted maximum likelihood estimators by a Monte Carlo simulation. The simulation studies show that the restricted estimates improve the mean squared errors remarkably, while the Mantel-Haenszel type estimates are competitive with the conditional maximum likelihood estimates, being slightly worse.     

Skew-normal alpha-power model

In this paper, authors study properties and inference for the newly introduced skew-normal alpha-power model, generalizing both, the power-normal and skew-normal models. Inference is approached via maximum likelihood. Fisher information matrix is derived and shown to be nonsingular at the whole parametric space. Special emphasis is placed on the special case of the power–skew-normal model. Studies with real data illustrate the fact that the model can be very useful in applications, being able to overfit less general models entertained in the literature.     

浅析“ICESCR”第2.1款“可获得最大化资源”的内涵

现今社会越来越多的人意识到,为推进人权目标的进一步实现,如何界定可获得的资源变得尤为重要,为此,国际社会各界也进行了激烈的讨论.在界定“可获得最大化资源”的定义时,很多人将其限定在经济领域,此种理解存在不足.虽然在实现人权的过程中金融资金和财政等资源是必不可少的,但一国所拥有的自然、教育以及公权力等资源也是推进人权目标实现所必需的,因此,对于可获得资源的多元化理解能够帮助一国更好地实现人权目标.     

Estimation of gaussian mixtures with rotationally invariant covariance matrices

Homoscedastic and heteroscedastic Gaussian mixtures differ in the constraints placed on the covariance matrices of the mixture components. A new mixture, called herein a strophoscedastic mixture, is defined by a new constraint, This constraint requires the matrices to be identical under orthogonal trans¬formations, where different transformations are allowed for different matrices. It is shown that the M-step of the EM method for estimating the parameters of strophoscedastic mixtures from sample data is explicitly solvable using singular value decompositions. Consequently, the EM-based maximum likelihood estimation algorithm is as easily implemented for strophoscedastic mixtures as it is for homoscedastic and heteroscedastic mixtures. An example of a “noisy” Archimedian spiral is presented.     

Computational algorithms for the factor model

Algorithms for computing the maximum likelihood estimators and the estimated covariance matrix of the estimators of the factor model are derived. The algorithms are particularly suitable for large matrices and for samples that give zero estimates of some error variances. A method of constructing estimators for reduced models is presented. The algorithms can also be used for the multivariate errors-in-variables model with known error covariance matrix.     

Estimating utility functions using generalized maximum entropy

This paper estimates von Neumann and Morgenstern utility functions using the generalized maximum entropy (GME), applied to data obtained by utility elicitation methods. Given the statistical advantages of this approach, we provide a comparison of the performance of the GME estimator with ordinary least square (OLS) in a real data small sample setup. The results confirm the ones obtained for small samples through Monte Carlo simulations. The difference between the two estimators is small and it decreases as the width of the parameter support vector increases. Moreover, the GME estimator is more precise than the OLS one. Overall, the results suggest that GME is an interesting alternative to OLS in the estimation of utility functions when data are generated by utility elicitation methods.     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

A robust procedure for testing an assumed value of the population correlation coefficient

For testing that the population correlations coefficientp Q, Tiku and Balakrishnan1986) developed a robust test. This test is extended here to situcitions where one wants to test that p p , p being a specified non-zero value of p. o o     

The power functions of the likelihood ratio tests for a simply ordered trend in normal means

Likelihood ratio tests for the homogeneity of k normal means with the alternative restricted by an increasing trend are considered as well as the likelihood ratio tests of the null hypothesis that the means satisfy the trend. While the work is primarily a survey of results concerning the power functions of these tests, the extensions of some results to the case of not necessarily equal sample sizes are presented. For the case of known or unknown population variances, exact expressions are given for the power functions for k=3,4, and approximations are discussed for larger k. The topics of consistency, bias and monotonicity of the power functions are included. Also, Bartholomew's conjectures concerning minimal and maximal powers are investigated, with results of a new numerical study given.