This paper studies a general family of methods for sufficient dimension reduction (SDR) called the test function (TF), based on the introduction of a nonlinear transformation of the response. By considering order 1 and 2 conditional moments of the predictors given the response, we distinguish...

A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrix-variate...

Many kernel-based learning algorithms have the computational load scaled with the sample size n due to the column size of a full kernel Gram matrix K. This article considers the Nyström low-rank approximation. It uses a reduced kernel K̂, which is n×m, consisting of m columns (say columns...

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback–Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived....

Let π denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring π. In...

This paper addresses, for a composite hypothesis about a subvector of the parameters in the parametric model, the issues posed by Rao and Mukerjee (1995) [22] and Li (2001) [14] on the power under a sequence of local alternatives. It is shown that a partially adjusted test statistic in a class...

Empirical and sequential empirical copula processes play a central role for statistical inference on copulas. However, as pointed out by Johan Segers [J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (3) (2012) 764–782] the usual...

The subject of this paper is the estimation of a probability measure on Rd from the data observed with an additive noise, under the Wasserstein metric of order p (with p≥1). We assume that the distribution of the errors is known and belongs to a class of supersmooth distributions, and we give...

It is shown that starting with a certain meaningful problem of the type “ranking of populations”, a need arises to employ functions which we call “Schur-convex of 2nd order with respect to two variables”. These functions L(v1,v2,v3,…,vn) are symmetric, and they are characterized in...

The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison et al. (2012) [5]). A major drawback of this max-stable model was the lack of a spectral representation such that...