VIF-based adaptive matrix perturbation method for heteroskedasticity-robust covariance estimators in the presence of multicollinearity

In this study, we investigate linear regression having both heteroskedasticity and collinearity problems. We discuss the properties related to the perturbation method. Important observations are summarized as theorems. We then prove the main result that states the heteroskedasticity-robust variances can be improved and that the resulting bias is minimized by using the matrix perturbation method. We analyze a practical example for validation of the method.     

区域的“城市性”与中国新型城市化道路

本文提出区域的“城市性”,对城市化涵义作出新的认识.考察中外城市化的演变史发现,城市化道路有两种类型:一是人口转移型城市化道路,二是结构转换型城市化道路,从中国的国情出发,借鉴中外城市化的经验教训,如今中国城市化发展道路的转型方向,应该是走人口转移和结构转型并存的“双轨”发展的新型城市化道路.     

浅谈矩阵特征值的估计

矩阵的特征值问题是矩阵计算的一个重要方向,在众多的领域中都得到了应用。在这样的大背景下,有必要深入地研究矩阵的特征值的估计问题。基于此,本文将结合国内外对于矩阵的特征值的估计方面的研究,以及一些具体的应用实例,来深入地探索矩阵的特征值的估计问题。     

On a characterization of the dispersion matrix based on the properties of regression

This paper provides a partial solution to a problem posed by J. Neyman (1965) regarding the characterization of multivariate negative binomial distribution based on the properties of regression. It is shown that some of the properties of regression characterize the form of the nonsingular dispersion matrix of the parent distribution, which, interestingly enough, corresponds to only two types viz. those of positive and negative multivariate binomial distributions.     

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.     

Performance of traditional f tests in repeated measures designs under covariance heterogeneity

This study investigates the performance of two traditional F tests, one for main effects and the other for interaction in repeated measures designs under several conditions of covariance heterogeneity. Overall, the test for interaction is more vulnerable than the one for main effects. Distortion in the level of significance is less serious for the case of equal group size.     

Regression for non-Euclidean data using distance matrices

Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.