Focused information criterion and model averaging based on weighted composite quantile regression

Ganggang Xu, Suojin Wang, Jianhua Z. Huang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non-parametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the frequentist model averaging WCQR-estimator of a focused parameter is a non-linear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. With properly chosen weights, the focused information criterion based WCQR estimators are not only robust to outliers and non-normal residuals but also can achieve efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedure.

Original languageEnglish (US)
Pages (from-to)365-381
Number of pages17
JournalScandinavian Journal of Statistics
Volume41
Issue number2
DOIs
StatePublished - Jun 2014
Externally publishedYes

Keywords

  • Focused information criterion
  • Frequentist model averaging
  • Model inference
  • Weighted composite quantile estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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