A continuous threshold expectile model

Feipeng Zhang, Qunhua Li

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. A continuous threshold expectile regression is developed for modeling data in which the effect of a covariate on the response variable is linear but varies below and above an unknown threshold in a continuous way. The estimators for the threshold and the regression coefficients are obtained using a grid search approach. The asymptotic properties for all the estimators are derived, and the estimator for the threshold is shown to achieve root-n consistency. A weighted CUSUM type test statistic is proposed for the existence of a threshold at a given expectile, and its asymptotic properties are derived under both the null and the local alternative models. This test only requires fitting the model under the null hypothesis in the absence of a threshold, thus it is computationally more efficient than the likelihood-ratio type tests. Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic cases. The application of the proposed method on a Dutch growth data and a baseball pitcher salary data reveals interesting insights. The proposed method is implemented in the R package cthreshER.

Original languageEnglish (US)
Pages (from-to)49-66
Number of pages18
JournalComputational Statistics and Data Analysis
Volume116
DOIs
StatePublished - Dec 1 2017

Fingerprint

Threshold Model
Wages
Data structures
Estimator
Statistics
Asymptotic Properties
Regression
Local Alternatives
Cumulative Sum
Data Modeling
Likelihood Ratio
Regression Coefficient
Null hypothesis
Test Statistic
Null
Covariates
Roots
Simulation Study
Vary
Grid

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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A continuous threshold expectile model. / Zhang, Feipeng; Li, Qunhua.

In: Computational Statistics and Data Analysis, Vol. 116, 01.12.2017, p. 49-66.

Research output: Contribution to journalArticle

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