Estimation and variable selection for generalized additive partial linear models
KAUST Grant NumberKUS-CI-016-04
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AbstractWe 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. © Institute of Mathematical Statistics, 2011.
CitationWang L, Liu X, Liang H, Carroll RJ (2011) Estimation and variable selection for generalized additive partial linear models. The Annals of Statistics 39: 1827–1851. Available: http://dx.doi.org/10.1214/11-AOS885.
SponsorsSupported by NSF Grant DMS-09-05730.Supported by a Merck Quantitative Sciences Fellowship Program.Supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherInstitute of Mathematical Statistics
JournalThe Annals of Statistics