On the foundations of parameter estimation for generalized partial linear models with B-splines and continuous optimization

Generalized linear models are widely used in statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms with a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2010-07, Vol.60 (1), p.134-143
Main Authors: Taylan, Pakize, Weber, Gerhard-Wilhelm, Liu, Lian, Yerlikaya-Özkurt, Fatma
Format: Article
Language:English
Subjects:
Additives
CMARS
Computer simulation
Conic quadratic programming
Conics
Flexibility
Foundations
Generalized partial linear models
Least squares method
Mathematical models
Maximum likelihood
Optimization
Penalty methods
Quadratic programming
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Summary:Generalized linear models are widely used in statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms with a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on the penalized maximum likelihood and the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines, which is attractive for nonparametric components. Then, we approach solving the P-IRLS problem using continuous optimization techniques. They have come to constitute an important complementary approach, alternative to the penalty methods, with flexibility for choosing the penalty parameter adaptively. In particular, we model and treat the constrained P-IRLS problem by using the elegant framework of conic quadratic programming. The method is illustrated using a small numerical example.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.04.040