Weak convergence for empirical processes of associated sequences
Weak convergence of a Dirichlet-multinomial process.
Weak convergence of linear rank statistics
Weak Hölder convergence of processes with application to the perturbed empirical process
We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample under a natural assumption about the regularity of the marginal distribution function F of the...
Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation
Weighted halfspace depth
Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.
Weighted uniform consistency of kernel density estimators with general bandwidth sequences.
Why view and what is next?
N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the view of density estimation. The Cencov’s work is available in Russian only and it hasn’t been translated, so late Igor Vajda decided to translate the Cencov’s paper and to add some remarks on the occasion of organizing the session “25 Years of the Density Estimation” at the Prague Stochastics 2010 Symposium. In this paper we...
Why minimax is not that pessimistic
In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...
Wild bootstrap in RCA(1) model
In the paper, a heteroskedastic autoregressive process of the first order is considered where the autoregressive parameter is random and errors are allowed to be non-identically distributed. Wild bootstrap procedure to approximate the distribution of the least-squares estimator of the mean of the random parameter is proposed as an alternative to the approximation based on asymptotic normality, and consistency of this procedure is established.