Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models

Baojiang Chen, Jing Qin

Research output: Contribution to journalArticle

Abstract

In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study.

Original languageEnglish (US)
Pages (from-to)1713-1722
Number of pages10
JournalStatistics in Medicine
Volume33
Issue number10
DOIs
StatePublished - May 10 2014

Fingerprint

Monotone Regression
Auxiliary Information
Empirical Likelihood
Isotonic Regression
Linear Models
Regression Model
Monotonicity
Covariates
Adjacent
Dementia
Missing Data
Monotonic
Statistical Analysis
Parameter Estimation
Simulation Study
Estimate
Demonstrate

Keywords

  • Auxiliary information
  • Empirical likelihood
  • Isotonic regression
  • Missing data

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

Cite this

Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models. / Chen, Baojiang; Qin, Jing.

In: Statistics in Medicine, Vol. 33, No. 10, 10.05.2014, p. 1713-1722.

Research output: Contribution to journalArticle

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