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2014 Integrated conditional moment test for partially linear single index models incorporating dimension-reduction
Shujie Ma, Jun Zhang, Zihua Sun, Hua Liang
Electron. J. Statist. 8(1): 523-542 (2014). DOI: 10.1214/14-EJS893


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.


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Shujie Ma. Jun Zhang. Zihua Sun. Hua Liang. "Integrated conditional moment test for partially linear single index models incorporating dimension-reduction." Electron. J. Statist. 8 (1) 523 - 542, 2014.


Published: 2014
First available in Project Euclid: 12 May 2014

zbMATH: 1348.62141
MathSciNet: MR3205732
Digital Object Identifier: 10.1214/14-EJS893

Primary: 62G08
Secondary: 62F12 , 62G20 , 62J02

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

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.8 • No. 1 • 2014
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