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Sliced Inverse Regression is a method for reducing the dimension of the explanatory variables x in non-parametric regression problems. Li (1991) discussed a version of this method which begins with a partition of the range of y into slices so that the conditional covariance matrix of x given y can be estimated by the sample covariance matrix within each(More)
Testing hypotheses on covariance matrices has long been of interest in statistics. The test of homogeneity is very often a preliminary step in discriminant analysis, cluster analysis, MANOVA, etc. In this article we propose nonparametric tests which are based on the eigenvalues of the differences among the sample covariance matrices after a common(More)
Algebraically, principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix, but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability. An attractive alternative in robust principal component analysis is to replace the classical(More)
Convex constraints (CCs) such as box constraints and linear inequality constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regression, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited(More)
Recently, Ng et al. (2009) studied a new family of distributions, namely the nested Dirichlet distributions. This family includes the traditional Dirichlet distribution as a special member and can be adopted to analyze incomplete categorical data. However, other important aspects of the family, such as marginal and conditional distributions and related(More)
The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for(More)