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Estimation and hypothesis test for partial linear multiplicative models

Jun Zhang, Zhenghui Feng and Heng Peng

Computational Statistics & Data Analysis, 2018, vol. 128, issue C, 87-103

Abstract: Estimation and hypothesis tests for partial linear multiplicative models are considered in this paper. A profile least product relative error estimation method is proposed to estimate unknown parameters. We employ the smoothly clipped absolute deviation penalty to do variable selection. A Wald-type test statistic is proposed to test a hypothesis on parametric components. The asymptotic properties of the estimators and test statistics are established. We also suggest a score-type test statistic for checking the validity of partial linear multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a non-central chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. We conduct simulation studies to demonstrate the performance of the proposed procedure and a real data is analyzed to illustrate its practical usage.

Keywords: Kernel smoothing; Local linear smoothing; Model checking; Partial linear models; Variable selection (search for similar items in EconPapers)
Date: 2018
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