Stability theorems for maxima of dependent sequences

Three stability theorems due to Gnedenko (1943), Barndorff-Nielsen (1963), and Tomkins (1986) are extended to the sample maxima of identically distributed ?-mixing and m-dependent sequences.     

Robust kernel estimators for additive models with dependent observations

Robust nonparametric estimators for additive regression or autoregression models under an α-mixing condition are proposed. They are based on local M-estimators or local medians with kernel weights, and their asymptotic behaviour is studied. Moreover, diese local M-estimators achieve the same univariate rate of convergence as their linear relatives.     

Asymptotic distribution of data-driven smoothers in density and regression estimation under dependence

We consider automatic data-driven density, regression and autoregression estimates, based on any random bandwidth selector h/_T. We show that in a first-order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidth h_T as long as h_T/h_T → 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.     

Conditional quantile estimation with auxiliary information for left-truncated and dependent data

In this paper, the empirical likelihood method is used to define a new estimator of conditional quantile in the presence of auxiliary information for the left-truncation model. The asymptotic normality of the estimator is established when the data exhibit some kind of dependence. It is assumed that the lifetime observations with multivariate covariates form a stationary α‐mixing sequence. The result shows that the asymptotic variance of the proposed estimator is not larger than that of standard kernel estimator. Finite sample behavior of the estimator is investigated via simulations too.     

A glimpse of the impact of pál erd#ous on probability and statistics

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdõs's contributions per se to probability‐statistics. He hopes to have succeeded in providing a guided tour of, and whenever it has appeared feasible, an introduction to, a few selected areas that have been strongly influenced by the work of Erdõs. The author also hopes to have succeeded in facilitating a glimpse of the impact of these contributions by presenting them in their historical context.