Electronic Journal of Statistics

Integrated conditional moment test for partially linear single index models incorporating dimension-reduction

Shujie Ma, Jun Zhang, Zihua Sun, and Hua Liang

Full-text: Open access

Abstract

Studying model checking problems for partially linear single-index models, we propose a variant of the integrated conditional moment test using a linear projection weighting function, which gains dimension reduction and makes the proposed method act as if there exists only one covariate even in the presence of multiple dimensional regressors. We derive asymptotic distributions of the proposed test; i.e., an integral of a centered Gaussian process under the null hypothesis and an integral of a non-centered one under Pitman local alternatives. We also suggest a consistent bootstrap procedure for calculating the critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for an illustration.

Article information

Source
Electron. J. Statist., Volume 8, Number 1 (2014), 523-542.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1399901043

Digital Object Identifier
doi:10.1214/14-EJS893

Mathematical Reviews number (MathSciNet)
MR3205732

Zentralblatt MATH identifier
1348.62141

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties 62J02: General nonlinear regression 62F12: Asymptotic properties of estimators

Keywords
Conditional moment test curse of dimensionality empirical process dimension reduction estimating function method linear projection projection direction smoothing-based tests

Citation

Ma, Shujie; Zhang, Jun; Sun, Zihua; Liang, Hua. Integrated conditional moment test for partially linear single index models incorporating dimension-reduction. Electron. J. Statist. 8 (2014), no. 1, 523--542. doi:10.1214/14-EJS893. https://projecteuclid.org/euclid.ejs/1399901043


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