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Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities
https://doi.org/10.32446/0368-1025it.2020-11-9-13
Abstract
An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.
About the Authors
A. V. Lapko
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences (ICM SB RAS);
Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Aleksandr V. Lapko
Krasnoyarsk
V. A. Lapko
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences (ICM SB RAS);
Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Vasiliy A. Lapko
Krasnoyarsk
References
1. Lapko A. V., Lapko V. A., Im S. T., Tuboltsev V. P., Avdeenok V. A., Optoelectronics, Instrumentation and Data Processing, 2019, vol. 55, no. 3, pp. 230–236. https://doi.org/10.3103/S8756699019030038
2. Lapko A. V., Lapko V. A., Computer Optics, 2019, vol. 43, no. 2, pp. 238–244. https://doi.org/10.18287/2412-6179-2019-43-2-238-244
3. Rudemo M., Scandinavian J. Statistics, 1982, no. 9, pp. 65–78.
4. Hall P., Annals of Statistics, 1983, vol. 11, pp. 1156–1174.
5. Silverman B. W. Density estimation for statistics and data analysis, London, Chapman & Hall, 1986, 175 p.
6. 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
7. Sheather S. J., Statistical Science, 2004, vol. 19, no. 4, pp. 588–597. https://doi.org/10.1214/088342304000000297
8. Terrell G. R., Scott D. W., Journal of the American Statistical Association, 1985, vol. 80, pp. 209–214.
9. Jones M. C., Marron J. S., Sheather S. J., Journal of the American Statistical Association, 1996, vol. 91, pp. 401–407.
10. Lapko A. V., Lapko V. A., Measurement Techniques, 2019, vol. 61, no. 10, pp. 979–986. https://doi.org/10.1007/s11018-019-01536-x
11. Epanechnikov V. A., Theory of Probability & Its Applications, 1969, vol. 14, no. 1, pp. 156–161.
12. Lapko A. V., Lapko V. A., Measurement Techniques, 2020, vol. 63, no. 3, pp. 171–176. https://doi.org/10.1007/s11018-020-01768-2
Review
For citations:
Lapko A.V., Lapko V.A. Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities. Izmeritel`naya Tekhnika. 2020;(11):9-13. (In Russ.) https://doi.org/10.32446/0368-1025it.2020-11-9-13
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