ESTIMATION AND VARIABLE SELECTION FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELS. Academic Article

abstract

• We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration.

authors

• Carroll, Raymond

published proceedings

• Ann Stat

altmetric score

• 0.5

author list (cited authors)

• Wang, L. i., Liu, X., Liang, H., & Carroll, R. J.

citation count

• 83

complete list of authors

• Wang, Li||Liu, Xiang||Liang, Hua||Carroll, Raymond J

publication date

• August 2011

publisher

• Institute of Mathematical Statistics  Publisher

published in

• ANNALS OF STATISTICS  Journal

keywords

• Backfitting
• Generalized Additive Models
• Generalized Partially Linear Models
• Lasso
• Nonconcave Penalized Likelihood
• Penalty-based Variable Selection
• Polynomial Spline
• Quasi-likelihood
• Scad
• Shrinkage Methods

PubMed Central ID

• 23243324

Digital Object Identifier (DOI)

• 10.1214/11-AOS885SUPP

URI

• https://hdl.handle.net/1969.1/185154

start page

• 1827

end page

• 1851

volume

• 39

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1214%2F11-aos885