Liu-type estimator in semiparametric partially linear additive models

Abstract

Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares (PL) approach and Liu estimation method, we propose a PL Liu estimator for the parametric component. When some additional linear restrictions on the parametric component are available, the corresponding restricted Liu estimator for the parametric component is constructed. The properties of the proposed estimators are derived. Some simulations are conducted to assess the performance of the proposed procedures and the results are satisfactory. Finally, a real data example is analysed.

Keywords:

• Liu estimator
• partially linear additive model
• profile least-squares approach
• restricted estimation

Mathematics Subject Classification (2000):

• 62G05
• 62J07

Acknowledgments

The authors would like to thank two anonymous referees and the Associate Editor for their constructed suggestions which significantly improved the presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Chuanhua Wei's research was supported by the National Natural Science Foundation of China [No. 11301565] and Beijing Higher Education Young Elite Teacher Project [No. YETP1316].