Journal
ANNALS OF STATISTICS
Volume 39, Issue 4, Pages 1827-1851Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AOS885
Keywords
Backfitting; generalized additive models; generalized partially linear models; LASSO; nonconcave penalized likelihood; penalty-based variable selection; polynomial spline; quasi-likelihood; SCAD; shrinkage methods
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Funding
- NSF [DMS-09-05730]
- Merck
- National Cancer Institute [CA57030]
- King Abdullah University of Science and Technology (KAUST) [KUS-CI-016-04]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0905730] Funding Source: National Science Foundation
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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.
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