We propose a new approach which generalizes and improves principal component analysis (PCA) and its recent advances. The approach is based on the following underlying ideas. PCA can be reformulated as a technique which provides the best linear estimator of the fixed rank for random vectors. By...

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28-30, 1990, pp. 63-78) has certain merits over the estimators derived through the...

Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite...

In this paper we propose two new descriptive measures for multivariate data: the effective variance and the effective dependence. These measures have a direct geometric and statistical interpretation and can be used to compare groups with different number of variables. The contribution of these...

One way of estimating a function from indirect, noisy measurements is to regularise an inverse of its Fourier transformation, using properties of the adjoint of the transform that degraded the function in the first place. It is known that when the function is smooth, this approach can perform...

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We...

In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available...

For a normally distributed random matrix Y with mean zero and general covariance matrix [Sigma]Y and for a symmetric matrix W, necessary and sufficient conditions are derived for the Wishartness of Y'WY.

This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably...

We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by...