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    Öğe
    ON FOUNDATIONS OF PARAMETER ESTIMATION FOR GENERALIZED PARTIAL LINEAR MODELS WITH B-SPLINES AND CONTINUOUS OPTIMIZATION
    (Amer Inst Physics, 2010) Taylan, Pakize; Weber, Gerhard-Wilhelm; Liu, Lian
    Generalized linear models are widely-used statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms by 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 penalized maximum likelihood and on 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 become an important complementary technology and alternative to the penalty methods with the flexibility of choosing the penalty parameter adaptively. In particular, we model and treat the constrained P-IRLS problem by the elegant framework of conic quadratic programming. This paper is of a more theoretical nature and a preparation of real-world applications in future.
  • [ X ]
    Öğe
    On the foundations of parameter estimation for generalized partial linear models with B-splines and continuous optimization
    (Pergamon-Elsevier Science Ltd, 2010) Taylan, Pakize; Weber, Gerhard-Wilhelm; Liu, Lian; Yerlikaya-Ozkurt, Fatma
    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.