Symmetric Location Estimation /Testing by Empirical Likelihood

Kyoungmi Kim, Mai Zhou

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The problem of estimating the center of a symmetric distribution is well studied and many nonparametric procedures are available. It often serves as the test problem for many nonparametric estimation procedures, and stimulated the development of efficient nonparametric estimation theory. We use this familiar setting to illustrate a novel use of empirical likelihood method for estimation and testing. Empirical likelihood is a general nonparametric inference method, see Owen [Owen, A. (2001). Empirical Likelihood. London: Chapman and Hall]. However, for symmetric location problem (and some other problems) empirical likelihood has difficulties. Owen (2001) call them "challenges for the empirical likelihood". We propose and study a way to use the empirical likelihood with such problems by modifying the parameter space. We illustrate this approach by applying it to the symmetric location problem. We show that the usual asymptotic theory of empirical likelihood still holds and the asymptotic efficiency of the so obtained empirical NPMLE of location is studied.

Original languageEnglish (US)
Pages (from-to)2233-2243
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Volume33
Issue number9 SPEC.ISS.
DOIs
StatePublished - Sep 2004
Externally publishedYes

Fingerprint

Location Estimation
Empirical Likelihood
Testing
Location Problem
Nonparametric Estimation
Nonparametric Inference
Estimation Theory
Asymptotic Efficiency
Symmetric Distributions
Efficient Estimation
Likelihood Methods
Asymptotic Theory
Test Problems
Parameter Space

Keywords

  • Asymptotic chi-square distribution
  • Many constraints of symmetry
  • Nonparametric information bound

ASJC Scopus subject areas

  • Statistics and Probability
  • Safety, Risk, Reliability and Quality

Cite this

Symmetric Location Estimation /Testing by Empirical Likelihood. / Kim, Kyoungmi; Zhou, Mai.

In: Communications in Statistics - Theory and Methods, Vol. 33, No. 9 SPEC.ISS., 09.2004, p. 2233-2243.

Research output: Contribution to journalArticle

@article{07f45df056794db5b7d7ec86ef601fea,
title = "Symmetric Location Estimation /Testing by Empirical Likelihood",
abstract = "The problem of estimating the center of a symmetric distribution is well studied and many nonparametric procedures are available. It often serves as the test problem for many nonparametric estimation procedures, and stimulated the development of efficient nonparametric estimation theory. We use this familiar setting to illustrate a novel use of empirical likelihood method for estimation and testing. Empirical likelihood is a general nonparametric inference method, see Owen [Owen, A. (2001). Empirical Likelihood. London: Chapman and Hall]. However, for symmetric location problem (and some other problems) empirical likelihood has difficulties. Owen (2001) call them {"}challenges for the empirical likelihood{"}. We propose and study a way to use the empirical likelihood with such problems by modifying the parameter space. We illustrate this approach by applying it to the symmetric location problem. We show that the usual asymptotic theory of empirical likelihood still holds and the asymptotic efficiency of the so obtained empirical NPMLE of location is studied.",
keywords = "Asymptotic chi-square distribution, Many constraints of symmetry, Nonparametric information bound",
author = "Kyoungmi Kim and Mai Zhou",
year = "2004",
month = "9",
doi = "10.1081/STA-200026602",
language = "English (US)",
volume = "33",
pages = "2233--2243",
journal = "Communications in Statistics - Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",
number = "9 SPEC.ISS.",

}

TY - JOUR

T1 - Symmetric Location Estimation /Testing by Empirical Likelihood

AU - Kim, Kyoungmi

AU - Zhou, Mai

PY - 2004/9

Y1 - 2004/9

N2 - The problem of estimating the center of a symmetric distribution is well studied and many nonparametric procedures are available. It often serves as the test problem for many nonparametric estimation procedures, and stimulated the development of efficient nonparametric estimation theory. We use this familiar setting to illustrate a novel use of empirical likelihood method for estimation and testing. Empirical likelihood is a general nonparametric inference method, see Owen [Owen, A. (2001). Empirical Likelihood. London: Chapman and Hall]. However, for symmetric location problem (and some other problems) empirical likelihood has difficulties. Owen (2001) call them "challenges for the empirical likelihood". We propose and study a way to use the empirical likelihood with such problems by modifying the parameter space. We illustrate this approach by applying it to the symmetric location problem. We show that the usual asymptotic theory of empirical likelihood still holds and the asymptotic efficiency of the so obtained empirical NPMLE of location is studied.

AB - The problem of estimating the center of a symmetric distribution is well studied and many nonparametric procedures are available. It often serves as the test problem for many nonparametric estimation procedures, and stimulated the development of efficient nonparametric estimation theory. We use this familiar setting to illustrate a novel use of empirical likelihood method for estimation and testing. Empirical likelihood is a general nonparametric inference method, see Owen [Owen, A. (2001). Empirical Likelihood. London: Chapman and Hall]. However, for symmetric location problem (and some other problems) empirical likelihood has difficulties. Owen (2001) call them "challenges for the empirical likelihood". We propose and study a way to use the empirical likelihood with such problems by modifying the parameter space. We illustrate this approach by applying it to the symmetric location problem. We show that the usual asymptotic theory of empirical likelihood still holds and the asymptotic efficiency of the so obtained empirical NPMLE of location is studied.

KW - Asymptotic chi-square distribution

KW - Many constraints of symmetry

KW - Nonparametric information bound

UR - http://www.scopus.com/inward/record.url?scp=7544235800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=7544235800&partnerID=8YFLogxK

U2 - 10.1081/STA-200026602

DO - 10.1081/STA-200026602

M3 - Article

AN - SCOPUS:7544235800

VL - 33

SP - 2233

EP - 2243

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 9 SPEC.ISS.

ER -