Preview

Izmeritel`naya Tekhnika

Advanced search
Open Access Open Access  Restricted Access Subscription Access

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

Vasiliy A. Lapko

Krasnoyarsk



A. V. Bakhtina
Reshetnev Siberian State University of Science and Technology
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

Views: 71


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