Preview

Izmeritel`naya Tekhnika

Advanced search
Open Access Open Access  Restricted Access Subscription Access

Analysis of optimization methods for nonparametric estimation of probability density in large volume samples

https://doi.org/10.32446/0368-1025it.2023-11-26-32

Abstract

A method is proposed for selecting the blurriness coefficient of kernel functions for nonparametric estimation of the probability density of a one-dimensional random variable with large volumes of statistical data, for example, obtained by remote sensing of natural objects. In the proposed method for selecting the blurriness coefficient, a regression estimate of the probability density is used. A method for synthesizing a regression probability density estimate is presented. The synthesis of the estimate is based on compression of the initial sample by decomposition of the range of values of a random variable. To decompose the range of values of a random variable, the Heinhold-Gaede rule and the formula for optimal selection of the number of sampling intervals are applied. Two approaches to the selection of the blurriness coefficient of the regression estimation of probability density using the traditional and proposed by the authors optimization methods of nonparametric estimation of probability density are considered. The traditional method of optimizing nonparametric estimation of probability density is based on minimizing its mean square deviation. In the proposed method, the selection of the blurriness coefficients of the kernel functions is based on the conditions of the minimum error of approximation of the regression estimate of the desired probability density. The approximation properties of the regression estimation of probability density using two methods of its optimization are analyzed. The conditions of their competence in estimating the probability densities of random variables with a lognormal distribution law are established. The results obtained allow for development when optimizing a regression estimate of the probability density of a multidimensional random variable.

About the Authors

A. V. Lapko
Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences; Reshetnev Siberian State University of Science and Technology
Russian Federation

Aleksandr V. Lapko

Krasnoyarsk



V. A. Lapko
Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences; Reshetnev Siberian State University of Science and Technology
Russian Federation

Vasiliy A. Lapko

Krasnoyarsk



References

1. Lapko A. V., Lapko V. A., Yadernye ocenki plotnosti veroyatnosti i ih primenenie [Kernel probability density estimates and their application], Krasnoyarsk, Reshetnev University Publ., 2021, 308 p. (In Russ.)

2. Lapko A. V., Lapko V. A., Optoelectronics, Instrumentation and Data Processing, 2014, vol. 50, no. 2, pp. 148–153. https://doi.org/10.3103/S875669901402006X

3. Rudemo M. Empirical choice of histogram and kernel density estimators, Scandinavian Journal of Statistics, 1982, no. 9, pp. 65–78.

4. Bowman A. W., Journal of Statistical Computation and Simulation, 1985, vol. 21, no. 3-4. https://doi.org/10.1080/00949658508810822

5. Hall P., Annals of Statistics, 1983, vol. 11(4), pp. 1156–1174. https://doi.org/10.1214/aos/1176346329

6. Jiang M., Provost S. B., Journal of Statistical Computation and Simulation, 2014, vol. 84, no. 3, pp. 614–627. https://doi.org/10.1080/00949655.2012.721366

7. Dutta S., Communications in Statistics – Simulation and Computation, 2016, vol. 45, no. 2, pp. 472–490. https://doi.org/10.1080/03610918.2013.862275

8. Sturges H. A., Journal of the American Statistical Association, 1926, vol. 21, pp. 65–66. https://doi.org/10.1080/01621459.1926.10502161

9. Storm R., Teoriya veroyatnostej. Matematicheskaya statistika. Statisticheskij kontrol’ kachestva [Probability theory. Mathematical statistics. Statistical quality control], Moscow, Mir Publ., 1970, 368 p. (In Russ.)

10. Heinhold I., Gaede K. W., Ingeniur statistic, München, Wien, Springler Verlag, 1964, 352 p. (In German)

11. Lapko A. V., Lapko V. A., Measurement Techniques, 2013, vol. 56, no. 7, pp. 763–767. https://doi.org/10.1007/s11018-013-0279-x

12. Lapko A. V., Lapko V. A., Measurement Techniques, 2020, vol. 63, no. 7, pp. 534–542. https://doi.org/10.1007/s11018-020-01820-1

13. Parzen E., Annals of Mathematical Statistics, 1962, vol. 33, nо. 3, pp. 1065–1076. https://doi.org/10.1214/aoms/1177704472

14. Epanechnikov V. A., Theory of Probability & Its Applications, 1969, vol. 14, no. 1, pp. 156–161. https://doi.org/10.1137/1114019

15. Gradov V. M., Ovechkin G. V., Ovechkin P. V., Rudakov I. V., Komp’yuternoe modelirovanie [Computer modeling], Moscow, Kurs, INFRA-M Publ., 2019, 264 p. (In Russ.)


Supplementary files

Review

For citations:


Lapko A.V., Lapko V.A. Analysis of optimization methods for nonparametric estimation of probability density in large volume samples. Izmeritel`naya Tekhnika. 2023;(11):26-32. (In Russ.) https://doi.org/10.32446/0368-1025it.2023-11-26-32

Views: 165


ISSN 0368-1025 (Print)
ISSN 2949-5237 (Online)