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Construction of \(D\)-optimal experimental designs for nonparametric regression models. (Russian, English) Zbl 1413.62122
Sib. Zh. Ind. Mat. 21, No. 2, 46-55 (2018); translation in J. Appl. Ind. Math. 12, No. 2, 234-242 (2018).
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.
62K05 Optimal statistical designs
62G08 Nonparametric regression and quantile regression
Full Text: DOI
[1] V. V. Fedorov, “Design of Experiments for Locally Weighted Regression,” J. Statist. Plann. Inference 81 (2), 363-382 (1999).
[2] V. V. Fedorov, Theory of Optimal Experiment (Nauka, Moscow, 1971) [in Russian].
[3] E. A. Nadaraja, “On Nonparametric Estimates of Density Functions and Regression Curves,” Theory Probab. Appl. 10 (1), 186-190 (1965).
[4] D. Rasin, “Nonparametric Econometrics: Introduction,” Kvantil’ No. 4, 7-56 (2008).
[5] G. S. Watson, “Smooth Regression Analysis,” Sankhya˜ Ser. A, 26 (4), 359-372 (1965).
[6] V. A. Epanechnikov, “Nonparametric Estimate of Multidimensional Probability Coefficient,” Theor. Veroyatnost. i Primenen. 14 (1), 156-161 (1969) [Theor. Probab. Appl. 14 (1), 153-158 (1969)].
[7] V. A. Fisher, “Optimal and Efficient Experimental Design for Nonparametric Regression with Application to Functional Data” (Univ. Press, Southampton, 2012), pp. 7-40.
[8] J. A. Nelder and R. Mead, “A Simplex Method for FunctionMinimization,” Comput. J. 7 (4), 308-313 (1965).
[9] R. Storn and K. Price, Differential Evolution: a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces, Technical Report TR-95-012, ICSI, March 1995 (ftp.icsi.berkeley.edu, 1995).
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