For a general class of order selection criteria, we establish analytic and non-asymptotic evaluations of both the underfitting and overfitting sets of selected models. These evaluations are further specified in various situations including regressions and autoregressions with finite or infinite...

In this article, we model multivariate categorical (binary and ordinal) response data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy tailed distributions. We consider both noninformative as well as informative prior distributions for...

This paper investigates the efficiencies of several generalized least squares estimators (GLSEs) in terms of the covariance matrix. Two models are analyzed: a seemingly unrelated regression model and a heteroscedastic model. In both models, we define a class of unbiased GLSEs and show that their...

The functional principal components analysis (PCA) involves new considerations on the mechanism of measuring distances (the norm). Some properties arising in functional framework (e.g., smoothing) could be taken into account through an inner product in the data space. But this proposed inner...

If a set of independent, identically distributed random vectors has heavy tails, so that the covariance matrix does not exist, there is no reason to expect that the sample covariance matrix conveys useful information. On the contrary, this paper shows that the eigenvalues and eigenvectors of the...

Additive models based on backfitting estimators are among the most important recent contributions to modern statistical modelling. However, the statistical properties of backfitting estimators have received relatively little attention. Recently, J.-D. Opsomer and D. Ruppert (1997,Ann....

Ann-dimensional random vector is said to have an[alpha]-symmetric distribution,[alpha]0, if its characteristic function is of the form[phi]((u1[alpha]+...+un[alpha])1/[alpha]). We study the classes[Phi]n([alpha]) of all admissible functions[phi]: [0, [infinity])--. It is known that members...

Let[Sigma]be an unknown covariance matrix. Perturbation (in)equalities are derived for various scale-invariant functionals of[Sigma]such as correlations (including partial, multiple and canonical correlations) or angles between eigenspaces. These results show that a particular confidence set...

A conditional test based on a Hotelling'sT2-type statistic is derived for significance of a multivariate mean having non-negative components. This test is shown to be uniformly more powerful than the unconditional test given by Silvapulle. The consistency and invariance of the new test are also...

We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is...