

Application of a nonparametric pattern recognition algorithm in the problem of testing the hypothesis about the independence of variables of ambiguous functions
https://doi.org/10.32446/0368-1025it.2022-01-17-22
Abstract
The problem of testing the hypothesis about the independence of two-dimensional random variables in the analysis of variable ambiguous functions is considered. To solve it, a technique is used based on a nonparametric pattern recognition algorithm of the kernel type corresponding to the maximum likelihood criterion. The use of this technique makes it possible to bypass the problem of decomposition of the range of values of random variables into intervals. Based on the results of computational experiments, the eff ectiveness of the applied technique was evaluated depending on the type of ambiguous functions, the level of random noise and the volume of initial statistical data. The results obtained are relevant for solving the problem of detecting natural and technical objects using remote sensing data.
About the Authors
A. V. LapkoRussian Federation
Aleksandr V. Lapko
Krasnoyarsk
V. A. Lapko
Russian Federation
Vasiliy A. Lapko
Krasnoyarsk
A. V. Bakhtina
Russian Federation
Anna V. Bakhtina
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. Trofi mova E. A., Kislyak N. V., Gilev D. V., Probability theory and mathematical statistics, Yekaterinburg, Ural Federal University Publ., 2018, 160 p. (In Russ.)
3. Lapko A. V., Lapko V. A., Optoelectronics, Instrumentation and Data Processing, 2021, vol. 57, no. 2, pp. 149–155. https://doi.org/10.3103/S8756699021020114
4. Zenkov I. V., Lapko A. V., Lapko V. A., Kiryushina E. V., Vokin V. N., Computer Optics, 2021, vol. 45, no 5, pp. 767–772. (In Russ.) https://doi.org/10.18287/2412-6179-CO-871
5. Lapko A. V., Lapko V. A., Measurement Techniques, 2021, vol. 64, no. 3, pp. 166–171. https://doi.org/10.1007/s11018-021-01914-4
6. Parzen E., Annals of Mathematical Statistics, 1962, vol. 33, nо. 3, pp. 1065-1076. https://doi.org/10.1214/aoms/1177704472
7. Epanechnikov V. A., Theory of Probability and Its Applications, 1969, vol. 14, no. 1, pp. 153–158. https://doi.org/10.1137/1114019
8. Rudemo M., Empirical Choice of Histograms and Kernel Density Estimators, Scandinavian Journal of Statistics, 1982, vol. 9, no. 2, pp. 65–78.
9. Bowman A. W., Journal of Statistical Computation and Simulation, 1985, vol. 21, pp. 313–327. https://doi.org/10.1080/00949658508810822
10. Hall P., Annals of Statistics, 1983, vol. 11, no. 4, pp. 1156– 1174. https://doi.org/10.1214/aos/1176346329
11. 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
12. Dutta S., Communications in Statistics – Simulation and Computation, 2016, vol. 45, no. 2, pp. 472-490. https://doi.org/10.1080/03610918.2013.862275
13. Heidenreich N.-B., Schindler A., Sperlich S., AStA Advances in Statistical Analysis, 2013, vol. 97, no. 4, pp. 403-433. https://doi.org/10.1007/s10182-013-0216-y
14. Li Q., Racine J. S., Nonparametric Econometrics: Theory and Practice, Princeton, Princeton University Press, 2007, 768 p.
15. 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
16. Duin R. P. W., IEEE Transactions on Computers, 1976, vol. 25, no. 11, pp. 1175–1179. https://doi.org/10.1109/TC.1976.1674577
17. Botev Z. I., Kroese D. P., Methodology and Computing in Applied Probability, 2008, vol. 10, no. 3, pp. 435-451. https://doi.org/10.1007/s11009-007-9057-z
18. Silverman B. W., Density estimation for statistics and data analysis, London, Chapman and Hall, 1986, 175 p.
19. Botev Z. I., Grotowski J. F., Kroese D. P., Annals of Statistics, 2010, vol. 38, no. 5, pp. 2916–2957. https://doi.org/10.1214/10-AOS799
20. Dobrovidov A. V., Ruds’ko I. M., Automation and Remote Control, 2010, vol. 71, no. 2, pp 209–224. https://doi.org/10.1134/S0005117910020050
21. O’Brien T. A., Kashinath K., Cavanaugh N. R., Collins W. D., O’Brien J. P., Computational Statistics and Data Analysis, 2016, vol. 101, pp. 148–160. https://doi.org/10.1016/j.csda.2016.02.014
22. Chen S., Journal of Probability and Statistics, 2015, vol. 2015, 242683. https://doi.org/10.1155/2015/242683
23. Scott D. W., Multivariate Density Estimation: Theory, Practice, and Visualization, New York, Wiley, 2015, 384 p.
24. Sharakshaneh А. S., Zheleznov I. G., Ivnitskij V. А., Complex system, Moscow, Vysshaya shkola Publ., 1977, 248 p. (In Russ.)
Review
For citations:
Lapko A.V., Lapko V.A., Bakhtina A.V. Application of a nonparametric pattern recognition algorithm in the problem of testing the hypothesis about the independence of variables of ambiguous functions. Izmeritel`naya Tekhnika. 2022;(1):17-22. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-01-17-22