Optimal convergence rates of nonparametric conditional quantiles in dependent cases
type: Item
instance of: scholarly article
title: Optimal convergence rates of nonparametric conditional quantiles in dependent cases
zbMATH Open document ID: 0827.62042
author: Peide Shi
author: Xuming He
published in: Chinese Science Bulletin
publication date: 1995-09-06T00:00:00Z
review text: Performance of statistical estimators often depends very much on model assumptions. It is desirable to see that optimal rates of convergence remain valid if there is some dependence structure in the data sequence. This note relaxes the independence assumption on the stationary sequence \(\{X_i, Y_i\}\). If the true conditional quantile function is smooth up to order \(r\) and the observed sequence is \(\beta\)-mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the \(B\)-spline based estimators and their derivatives.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62G07
zbMATH DE Number: 783506
zbMATH Keywords: B-spline based estimators
zbMATH Keywords: nonparametric regression quantiles
zbMATH Keywords: beta mixing
zbMATH Keywords: model assumptions
zbMATH Keywords: dependence structure
zbMATH Keywords: stationary sequence
zbMATH Keywords: conditional quantile function
zbMATH Keywords: optimal global convergence rates
zbMATH Keywords: derivatives
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 783506