Estimation and hypothesis test for partial linear multiplicative models

Jun Zhang, Zhenghui Feng*, Heng Peng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)87-103
Number of pages17
JournalComputational Statistics and Data Analysis
Publication statusPublished - Dec 2018

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Kernel smoothing
  • Local linear smoothing
  • Model checking
  • Partial linear models
  • Variable selection


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