Let (X,Y),(X1,Y1),(X2,Y2),... denote independent positive random vectors with common distribution function F(x,y)=P(X[less-than-or-equals, slant]x,Y[less-than-or-equals, slant]y) with F(x,y)1 for all x,y. Based on the Xi and the Yj we construct the sum sequences and respectively. For a double...

The Fisher information for the canonical link exponential family generalised linear mixed model is derived. The contribution from the fixed effects parameters is shown to have a particularly simple form.

The copula density is estimated using Bernstein-Kantorovich polynomials. The estimator is the usual one based on the smoothed histogram. Strong consistency is obtained in L1 and pointwise almost everywhere, allowing for dependent data. For L1 convergence, no condition is imposed on the copula...

A nonparametric test of the mutual independence between many numerical random vectors is proposed. This test is based on a characterization of mutual independence defined from probabilities of half-spaces in a combinatorial formula of Möbius. As such, it is a natural generalization of tests of...

This work studies the effects of sampling variability in Monte Carlo-based methods to estimate very high-dimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely high-dimensional systems, various...

The estimation of a regression function by kernel method for longitudinal or functional data is considered. In the context of longitudinal data analysis, a random function typically represents a subject that is often observed at a small number of time points, while in the studies of functional...

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current...

Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this...

A recently proposed method for the pairwise comparison of arbitrary independent random variables results in a probabilistic relation. When restricted to discrete random variables uniformly distributed on finite multisets of numbers, this probabilistic relation expresses the winning probabilities...

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It...