Estimation and hypothesis test for partial linear single-index multiplicative models

Jun Zhang (), Xia Cui () and Heng Peng ()
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Jun Zhang: Shenzhen University
Xia Cui: Guangzhou University
Heng Peng: The Hong Kong Baptist University

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 3, No 4, 699-740

Abstract: Abstract Estimation and hypothesis test for partial linear 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. To test a hypothesis on the parametric components, a Wald-type test statistic is proposed. We employ the smoothly clipped absolute deviation penalty to select relevant variables. To study model checking problem, we propose a variant of the integrated conditional moment test statistic by using linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for illustration.

Keywords: Local linear smoothing; Model checking; Profile least product relative error estimator; Single-index; Variable selection (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10463-019-00706-6

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