Parallel principal axes are introduced and used to investigate the structure of multivariate distributions. In the class of elliptical distributions, it is shown that self-consistency of parallel principal axes characterizes normality. Parallel principal axes are used to illustrate the...

Correlation coefficients have many applications for studying the relationship among multivariate observations. Classical inferences on correlation coefficients are mainly based on the normality assumption. This assumption is hardly realistic in the real world, which implies that the procedures...

The varying-coefficient model is an attractive alternative to the additive and other models. One important method in estimating the coefficient functions in this model is the local polynomial fitting approach. In this approach, the choice of bandwidth is crucial. If the unknown curve is spatial...

Let the column vectors of X:: M-N, MN, be distributed as independent complex normal vectors with the same covariance matrix [Sigma]. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLXH where L: N-N is a positive definite hermitian matrix. This paper deals with...

In this study bivariate kernel density estimators are considered when a component is subject to random truncation. In bivariate truncation models one observes the i.i.d. samples from the triplets (T, Y, X) only if T[less-than-or-equals, slant]Y. In this set-up, Y is said to be left...

Consider the quadratic form Z=YH(XLXH)-1 Y where Y is a p-m complex Gaussian matrix, X is an independent p-n complex Gaussian matrix, L is a Hermitian positive definite matrix, and m[less-than-or-equals, slant]p[less-than-or-equals, slant]n. The distribution of Z has been studied for over 30...

In this paper we solve two open problems posed by Joe (1997) concerning the supermodular order. First we give an example which shows that the supermodular order is strictly stronger than the concordance order for dimension d=3. Second we show that the supermodular order fulfils all desirable...

We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.

Theoretical accuracies are studied for asymtotic approximations of the expected probabilities of misclassification (EPMC) when the linear discriminant function is used to classify an observation as coming from one of two multivariate normal populations with a common covariance matrix. The...

We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in...