Electronic Journal of Statistics

Maximum empirical likelihood estimation and related topics

Hanxiang Peng and Anton Schick

Full-text: Open access

Abstract

This article develops a theory of maximum empirical likelihood estimation and empirical likelihood ratio testing with irregular and estimated constraint functions that parallels the theory for parametric models and is tailored for semiparametric models. The key is a uniform local asymptotic normality condition for the local empirical likelihood ratio. This condition is shown to hold under mild assumptions on the constraint function. Applications of our results are discussed to inference problems about quantiles under possibly additional information on the underlying distribution and to residual-based inference about quantiles.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 2962-2994.

Dates
Received: February 2017
First available in Project Euclid: 19 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1537344589

Digital Object Identifier
doi:10.1214/18-EJS1471

Subjects
Primary: 62G05: Estimation
Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties

Keywords
Irregular and estimated constraints nuisance parameters empirical likelihood ratio tests uniform local asymptotic normality condition

Rights
Creative Commons Attribution 4.0 International License.

Citation

Peng, Hanxiang; Schick, Anton. Maximum empirical likelihood estimation and related topics. Electron. J. Statist. 12 (2018), no. 2, 2962--2994. doi:10.1214/18-EJS1471. https://projecteuclid.org/euclid.ejs/1537344589


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