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, cilt.60, sa.1, ss.134-143, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 60 Sayı: 1
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.camwa.2010.04.040
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.134-143
  • Anahtar Kelimeler: Generalized partial linear models, Maximum likelihood, Penalty methods, Conic quadratic programming, CMARS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.