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An unconventional method for selecting the blur coefcients of kernel functions in nonparametric regression
https://doi.org/10.32446/0368-1025it.2022-2-3-7
Abstract
The traditional method for selecting the blur coefficients of kernel functions in nonparametric regression is based on minimizing the root mean square error in the approximation of the desired dependence from the initial statistical data. With an increase in the volume of the training sample of the values of the variables of the restored dependence, the computational costs of optimizing nonparametric regression increase signifi cantly. An unconventional method for selecting the nonparametric regression blurriness coeffi cients optimal for the kernel probability densities of the variables of the recovered dependence is proposed. Statistical estimates of the mean square deviations of the joint probability density of the variables of the restored dependence were used as an optimality criterion for selecting the blur coefficients of kernel probability densities. The proposed technique made it possible to avoid calculating the approximation error of the restored dependence by nonparametric regression, which is confi rmed by the results of computational experiments. The results obtained make it possible to use the method of fast optimization of kernel estimates of probability densities in the synthesis of nonparametric regression.
About the Authors
A. V. Lapko
Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences; Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Aleksandr V. Lapko
Krasnoyarsk
A. V. Lapko
Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences; Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Vasiliy A. Lapko
Krasnoyarsk
References
1. Zenkov I. V., Lapko A. V., Lapko V. A., Im S. T., Tuboltsev V. P., Avdeenok V. L., Computer Optics, 2021, vol. 45, no 2, pp. 253– 260. (In Russ.) https://doi.org/10.18287/2412-6179-CO-801
2. Lapko A. V., Lapko V. A., Optoelectronics, Instrumentation and Data Processing, 2010, vol. 46, no 1, pp. 56–63. https://doi.org/10.3103/S8756699010010073.
3. Varzhapetyan A. G., Mikhailova E. Yu., Metody vybora opredelyayushchikh kharakteristik neparametricheskikh algoritmov identifi katsii modelei nadezhnosti slozhnykh sistem po ekspluatatsionnym dannym, Voprosy kibernetiki, vol. 094, Statisticheskie metody v teorii obespecheniya ekspluatatsii, ed. S. F. Levin., Moscow, AN SSSR, Nauchnyi sovet po kompleksnoi probleme Kibernetika, 1982, pp. 77–87. (In Russ.)
4. Silverman B. W., Density estimation for statistics and data analysis, London, Chapman and Hall, 1986, 175 p.
5. Sheather S., Jones M., Journal of Royal Statistical Society Series B, 1991, vol. 53, no. 3, pp. 683–690. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x
6. Sheather S. J., Statistical Science, 2004, vol. 19, no. 4, pp. 588–597. https://doi.org/10.1214/088342304000000297
7. Terrell G. R., Scott D. W., Journal of the American Statistical Association, 1985, vol. 80, pp. 209–214. https://doi.org/10.2307/2288074
8. Jones M. C., Marron J. S., Sheather S. J., Journal of the American Statistical Association, 1996, vol. 91, pp. 401–407. https://doi.org/10.2307/2291420
9. Scott D. W. Multivariate Density Estimation: Theory, Practice, and Visualization, New York, Wiley, 1992, 317 p.
10. Lapko A. V., Lapko V. A., Measurement Techniques, 2021, vol. 63, no. 11, pp. 856–861. https://doi.org/10.1007/s11018-021-01873-w
11. Lapko A. V., Lapko V. A., Measurement Techniques, 2021, vol. 64, no. 1, pp. 13–20. https://doi.org/10.1007/s11018-021-01889-2
12. Lapko A. V., Lapko V. A., Measurement Techniques, 2019, vol. 62, no. 8, pp. 665–672. https://doi.org/10.1007/s11018-019-01676-0
13. Härdle W., Applied Nonparametric Regression, Cambridge University Press, 1990, 434 p.
14. Nadaraya E. A., Neparametricheskie otsenki krivoi regressii, Proceedings of the Computer C enter of the USSR Academy of Sciences, 1965, issue 5, pp. 56–68. (In Russ.)
15. Rudemo M., Empirical Choice of Histograms and Kernel Density Estimators, Scandinavian Journal of Statistics, 1982, no.9, pp. 65–78.
16. Bowman A. W., Journal of Statistical Computation and Simulation, 1985, vol. 21, pp. 313–327. https://doi.org/10.1080/00949658508810822
17. Hall P., Annals of Statistics, 1983, vol. 11, no. 4, pp. 1156–1174. https://doi.org/10.1214/aos/1176346329
18. Lapko A. V., Lapko V. A., Measurement Techniques, 2017, vol. 60, no. 6, pp. 515–522. https://doi.org/10.1007/s11018-017-1228-x
19. Gmurman V. E., Probability theory and mathematical statistics, Moscow, Vysshaya shkola Publisher, 1999, 479 p. (In Russ.)
20. Epanechnikov V. A., Theory of Probability & Its Applications, 1969, vol. 14, no. 1, pp. 153–158. https://doi.org/10.1137/1114019
Review
For citations:
Lapko A.V., Lapko A.V. An unconventional method for selecting the blur coefcients of kernel functions in nonparametric regression. Izmeritel`naya Tekhnika. 2022;(2):3-7. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-2-3-7
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