Empirical likelihood inferences for the semiparametric additive isotonic regression

Guang Cheng, Yichuan Zhao, Bo Li

Research output: Contribution to journalArticle

Abstract

We consider the (profile) empirical likelihood inferences for the regression parameter (and its any sub-component) in the semiparametric additive isotonic regression model where each additive nonparametric component is assumed to be a monotone function. In theory, we show that the empirical log-likelihood ratio for the regression parameters weakly converges to a standard chi-squared distribution. In addition, our simulation studies demonstrate the empirical advantages of the proposed empirical likelihood method over the normal approximation method in Cheng (2009) [4] in terms of more accurate coverage probability when the sample size is small. It is worthy pointing out that we can construct the empirical likelihood based confidence region without the hassle of tuning any smoothing parameter due to the shape constraints assumed in this paper.

Original languageEnglish (US)
Pages (from-to)172-182
Number of pages11
JournalJournal of Multivariate Analysis
Volume112
DOIs
StatePublished - Nov 1 2012

Fingerprint

Isotonic Regression
Likelihood Inference
Empirical Likelihood
Tuning
Regression
Shape Constraint
Chi-squared distribution
Profile Likelihood
Log-likelihood Ratio
Normal Approximation
Confidence Region
Likelihood Methods
Smoothing Parameter
Monotone Function
Coverage Probability
Approximation Methods
Regression Model
Sample Size
Simulation Study
Converge

Keywords

  • Confidence region
  • Empirical likelihood
  • Isotonic regression
  • Semiparametric additive model

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

Empirical likelihood inferences for the semiparametric additive isotonic regression. / Cheng, Guang; Zhao, Yichuan; Li, Bo.

In: Journal of Multivariate Analysis, Vol. 112, 01.11.2012, p. 172-182.

Research output: Contribution to journalArticle

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