Construction of D-Optimal Experimental Designs for Nonparametric Regression Models

Under study is the problem of a D -optimal experimental design for the problem of nonparametric kernel smoothing. Modification is proposed for the process of calculating the Fisher information matrix. D -optimal designs are constructed for one and several target points for the problems of nonparamet...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2018-04, Vol.12 (2), p.234-242
Main Authors: Denisov, V. I., Timofeev, V. S., Kamenev, P. A.
Format: Article
Language:English
Subjects:
Algorithms
Design modifications
Fisher information
Kernels
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonparametric statistics
Optimality criteria
Optimization
Regression analysis
Regression models
Smoothing
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Summary:Under study is the problem of a D -optimal experimental design for the problem of nonparametric kernel smoothing. Modification is proposed for the process of calculating the Fisher information matrix. D -optimal designs are constructed for one and several target points for the problems of nonparametric kernel smoothing using a uniform kernel, the Gauss and Epanechnikov kernels. Comparison is performed between Fedorov’s algorithm and direct optimization methods (such as the Nelder–Mead method and the method of differential evolution). The features of the application of the optimality criterion for the experimental design of the problems with several target points were specified for the cases of various kernels and bandwidths.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478918020047