Estimation and hypothesis test for single-index multiplicative models

Jun Zhang (), Junpeng Zhu () and Zhenghui Feng ()
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Jun Zhang: Shenzhen University
Junpeng Zhu: Shenzhen University
Zhenghui Feng: Xiamen University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 1, No 14, 242-268

Abstract: Abstract Estimation and hypothesis tests for single-index multiplicative models are considered in this paper. To estimate unknown single-index parameter, we propose a profile least product relative error estimator coupled with a leave-one-component-out method. For the hypothesis testing of parametric components, a Wald-type test statistic is proposed. The asymptotic properties of the estimators and test statistics are established, and a smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. A score-type test statistic is then proposed for checking the validity of single-index multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a noncentral chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.

Keywords: Kernel smoothing; Local linear smoothing; Model checking; Single index; Variable selection; 62G05; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11749-018-0586-2

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