Bahadur Representation for the Nonparametric M-Estimator Under alpha-mixing Dependence

Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence

A general result on the performance of the wavelet hard thresholding estimator under α-mixing dependence

Abstract: In this note, we consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a wavelet hard thresholding estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are g...

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” (Efron, 1967) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of c...

Multivariate Spatial U-Quantiles: a Bahadur-Kiefer Representation, a Theil-Sen Estimator for Multiple Regression, and a Robust Dispersion Estimator

A leading multivariate extension of the univariate quantiles is the so-called “spatial” or “geometric” notion, for which sample versions are highly robust and conveniently satisfy a Bahadur-Kiefer representation. Another extension of univariate quantiles has been to univariate U-quantiles, on the basis of which, for example, the well-known Hodges-Lehmann location estimator has a natural formula...

Weak Dependence beyond Mixing and Asymptotics for Nonparametric Regression