Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the "curse of dimensionality". To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index...

This paper deals with the problem of estimating the mean matrix in an elliptically contoured distribution with unknown scale matrix. The Laplace and inverse Laplace transforms of the density allow us not only to evaluate the risk function with respect to a quadratic loss but also to simplify...

In this paper we aim to construct adaptive confidence region for the direction of [xi] in semiparametric models of the form Y=G([xi]TX,[epsilon]) where G([dot operator]) is an unknown link function, [epsilon] is an independent error, and [xi] is a pnx1 vector. To recover the direction of [xi],...

In this note, we revisit the single-index model with heteroscedastic error, and recommend an estimating equation method in terms of transferring restricted least squares to unrestricted least squares: the estimator of the index parameter is asymptotically more efficient than existing estimators...

Accurate distributions of the estimator of the tetrachoric correlation coefficient and, more generally, functions of sample proportions for the 2 by 2 contingency table are derived. The results are obtained given the definitions of the estimators even when some marginal cell(s) are empty. Then,...

Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. Illustrations are provided and...

Van Trees' Bayesian version of the Cramér-Rao inequality is generalised here to the context of smooth loss functions on manifolds and estimation of parameters of interest. This extends the multivariate van Trees inequality of Gill and Levit (1995) [R.D. Gill, B.Y. Levit, Applications of the van...

In this paper, we consider a class of nonlinear autoregressive (AR) processes with state-dependent switching, which are two-component Markov processes. The state-dependent switching model is a nontrivial generalization of Markovian switching formulation and it includes the Markovian switching as...

We use a recent characterization of the d-dimensional Archimedean copulas as the survival copulas of d-dimensional simplex distributions (McNeil and Neslehová (2009) [1]) to construct new Archimedean copula families, and to examine the relationship between their dependence properties and the...

The stereological problem of unfolding the sphere size distribution from linear sections is considered. A minimax estimator of the intensity function of a Poisson process that describes the problem is introduced and an adaptive estimator is constructed that achieves the optimal rate of...