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

TAYLAN P., Weber G., Liu L., Yerlikaya-Ozkurt F.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.60, no.1, pp.134-143, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1016/j.camwa.2010.04.040
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.134-143
  • Keywords: Generalized partial linear models, Maximum likelihood, Penalty methods, Conic quadratic programming, CMARS
  • Middle East Technical University Affiliated: Yes

Abstract

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-IRIS problem by using the elegant framework of conic quadratic programming. The method is illustrated using a small numerical example. (C) 2010 Elsevier Ltd. All rights reserved.