Asymptotics of nonparametric L-1 regression models with dependent data

Research output: Contribution to journalArticle

Abstract

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

Original languageEnglish (US)
Pages (from-to)1532-1559
Number of pages28
JournalBernoulli
Volume20
Issue number3
DOIs
StatePublished - Aug 2014

Fingerprint

Dependent Data
Bahadur Representation
Regression Model
Quantile
Weighted Empirical Processes
Estimate
Least Absolute Deviation
Scale Function
Progesterone
Correlated Data
Dependence Structure
Nonparametric Model
Modulus of Continuity
Nonparametric Regression
Longitudinal Data
Asymptotic Properties
Asymptotic Behavior
kernel

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

@article{89d449aa157243b08a91783eb6f9d61e,
title = "Asymptotics of nonparametric L-1 regression models with dependent data",
abstract = "We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.",
author = "Zhibiao Zhao and Ying Wei and Lin, {Dennis K.J.}",
year = "2014",
month = "8",
doi = "10.3150/13-BEJ532",
language = "English (US)",
volume = "20",
pages = "1532--1559",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "3",

}

Asymptotics of nonparametric L-1 regression models with dependent data. / Zhao, Zhibiao; Wei, Ying; Lin, Dennis K.J.

In: Bernoulli, Vol. 20, No. 3, 08.2014, p. 1532-1559.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotics of nonparametric L-1 regression models with dependent data

AU - Zhao, Zhibiao

AU - Wei, Ying

AU - Lin, Dennis K.J.

PY - 2014/8

Y1 - 2014/8

N2 - We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

AB - We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

UR - http://www.scopus.com/inward/record.url?scp=84903939673&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903939673&partnerID=8YFLogxK

U2 - 10.3150/13-BEJ532

DO - 10.3150/13-BEJ532

M3 - Article

AN - SCOPUS:84903939673

VL - 20

SP - 1532

EP - 1559

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 3

ER -