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

  • Authors:

  • Pakize Taylan;Gerhard-Wilhelm Weber;Lian Liu;Fatma Yerlikaya-Özkurt

  • Affiliations:

  • Dicle University, Department of Mathematics, 21280 Diyarbakır, Turkey;Middle East Technical University, Institute of Applied Mathematics, 06531 Ankara, Turkey;Roche Pharma Development Center in Asia Pacific, 1100 LongDong Ave, Shanghai, 201203, China;Middle East Technical University, Institute of Applied Mathematics, 06531 Ankara, Turkey

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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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-IRLS problem by using the elegant framework of conic quadratic programming. The method is illustrated using a small numerical example.