ON FOUNDATIONS OF PARAMETER ESTIMATION FOR GENERALIZED PARTIAL LINEAR MODELS WITH B-SPLINES AND CONTINUOUS OPTIMIZATION

Date

2010-02-04

Author

TAYLAN, PAKİZE
Weber, Gerhard Wilhelm
Liu, Lian

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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.

Subject Keywords

Regression, Generalized Linear Models, Generalized Partial Linear Models, Generalized Additive Model, Least Squares, Maximum Likelihood, Curvature, Newton-Rapshon Algorithm, Penalty Methods, Continuous Optimization, Conic Quadratic Programming

URI

https://hdl.handle.net/11511/56528

DOI

https://doi.org/10.1063/1.3459763

Conference Name

3rd Global Conference on Power Control and Optimization

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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Citation Formats

P. TAYLAN, G. W. Weber, and L. Liu, “ON FOUNDATIONS OF PARAMETER ESTIMATION FOR GENERALIZED PARTIAL LINEAR MODELS WITH B-SPLINES AND CONTINUOUS OPTIMIZATION,” Gold Coast, AUSTRALIA, 2010, vol. 1239, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56528.