Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood

Abstract

Varying coefficient models (VCMs) allow us to generalise standard linear regression models to incorporate complex covariate effects by modelling the regression coefficients as functions of another covariate. For nonparametric varying coefficients, we can borrow the idea of parametrically guided estimation to improve asymptotic bias. In this paper, we develop a guided estimation procedure for the nonparametric VCMs. Asymptotic properties are established for the guided estimators and a method of bandwidth selection via bias-variance tradeoff is proposed. We compare the performance of the guided estimator with that of the unguided estimator via both simulation and real data examples.

Keywords:

• generalised linear models
• local polynomial smoothing
• nonparametric regression
• parametrically guided estimation
• varying coefficient model

AMS Subject Classification:

• 62J12
• 62G08

Acknowledgements

We thank two anonymous referees, an anonymous Associate Editor and the editor for their constructive and helpful comments, which has improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Maity's research was supported by NIH grant [R00 ES017744] and a NCSU Faculty Research and Professional Development (FRPD) grant. Wu's research was partially supported by NSF grant [DMS-1055210] and NIH grant [R01-CA149569].