SPLINE REGRESSION WITH VARIABLE PENALTY COEFFICIENTS
V. I. Denisov, A. V. Faddeenkov
Novosibirsk State Technical University, pr. Karla Marksa 20, Novosibirsk 630073, Russia
Keywords: параметрические и непараметрические методы, полупараметрическая регрессия, модели штрафных сплайнов, модели компонент дисперсии, parametric and nonparametric methods, semi-parametric regression, penalty spline models, variance component models
Abstract
The problem of constructing a semi-parametric spline regression model is considered. A new model of penalty splines with variable penalty coefficients is proposed. In the model, it is assumed that the coordinates of the basis points are determined by solving the optimization problem of minimizing the residual sum of squares. The choice of values of the penalty coefficients is based on the representation of the original model in the form of a random-effects model (variance component model). A series of computer simulation experiments was performed to reconstruct the regression line with different noise levels and in the presence of outliers. The results of computational experiments to reconstruct the regression line are presented that show greater accuracy of the new model in comparison with conventional models.
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