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Application of a Nonparametric Pattern Recognition Algorithm to the Problem of Testing the Hypothesis of the Independence of Variables of Multi-Valued Functions

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Measurement Techniques Aims and scope

The problem of hypothesis testing for the independence of two-dimensional random variables in the analysis of variables of multi-valued functions is considered. To solve it, we used a technique based on a nonparametric kernel-type pattern recognition algorithm corresponding to the maximum likelihood criterion. The technique made it possible to bypass the problem of decomposing the random variable domain of values into intervals. Based on the results of computational experiments, the effectiveness of the applied technique was estimated depending on the type of multi-valued functions, the level of random noise and the amount of initial statistical data. The results obtained are relevant for solving the problem of detecting natural and technical objects from remote sensing data.

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References

  1. I. V. Zenkov, A. V. Lapko, V. A. Lapko, et al., “Nonparametric algorithm for automatic classification of large volume multidimensional statistical data and its application,” Comp. Opt., 45, No. 2, 253–260 (2021), 10.18287/2412-6179-CO-801.

  2. E. A. Trofimova, N. V. Kislyak, and D. V. Gilev, Probability Theory and Mathematical Statistics: Textbook, Ural Federal University Press, Ekaterinburg (2018).

    Google Scholar 

  3. A. V. Lapko and V. A. Lapko, “Testing the hypothesis about the independence of two-dimensional random variables using a nonparametric pattern recognition algorithm,” Avtometriya, 57, No. 2, 41–48 (2021), https://doi.org/10.15372/AUT20210205.

  4. I. V. Zenkov, A. V. Lapko, V. A. Lapko, et al., “Nonparametric pattern recognition algorithm in the problem testing the hypothesis of the independence of random variables,” Comp. Opt., 45, No. 5, 767–772 (2021), https://doi.org/10.18287/2412-6179-CO-871.

  5. A. V. Lapko and V. A. Lapko, “Analysis of the ratio of standard deviations of the kernel estimate of the probability density under conditions of independent and dependent random variables,” Izmer. Tekhn., No. 3, 9–14 (2021), 10.32446/0368-1025it.2021-3-9-14.

  6. E. Parzen, Ann. Math. Stat., 33, No. 3, 1065–1076 (1962), https://doi.org/10.1214/aoms/1177704472.

    Article  Google Scholar 

  7. V. A. Epanechnikov, “Nonparametric estimation of multidimensional probability density,” Teor. Veroyatn. Primen., 14, No. 1, 156–161 (1969).

    MathSciNet  MATH  Google Scholar 

  8. M. Rudemo, “Empirical choice of histograms and kernel density estimators,” Scand. J. Stat., 9, No. 2, 65–78 (1982).

  9. A. W. Bowman, J. Stat. Comp. Simul., 21, 313–327 (1985), https://doi.org/10.1080/00949658508810822.

    Article  Google Scholar 

  10. P. Hall, Ann. Stat., 11, No. 4, 1156–1174 (1983), https://doi.org/10.1214/aos/1176346329.

    Article  Google Scholar 

  11. M. Jiang and S. B. Provost, J. Stat. Comp. Simul., 84, No. 3, 614–627 (2014), https://doi.org/10.1080/009.

    Article  Google Scholar 

  12. S. Dutta, Comm. Stat.-Simul. Comp., 45, No. 2, 472–490 (2016), https://doi.org/10.1080/03610918.2013.862275.

    Article  Google Scholar 

  13. N.-B. Heidenreich, A. Schindler, and S. Sperlich, AStA Adv. Stat. Anal., 97, No. 4, 403–433 (2013), https://doi.org/10.1007/s10182-013-0216-y.

    Article  MathSciNet  Google Scholar 

  14. Q. Li and J. S. Racine, Nonparametric Econometrics: Theory and Practice, Princeton University Press, Princeton (2007).

    MATH  Google Scholar 

  15. A. V. Lapko and V. A. Lapko, “Analysis of methods for optimizing nonparametric estimation of the probability density using a kernel function blur coefficient,” Izmer. Tekhn., No. 6, 3–8 (2017).

    Google Scholar 

  16. R. P. W. Duin, IEEE T. Comp., 25, No. 11, 1175–1179 (1976), https://doi.org/10.1109/TC.1976.1674577.

    Article  Google Scholar 

  17. Z. I. Botev and D. P. Kroese, Method. Comp. Appl. Probab., 10, No. 3, 435–451 (2008), https://doi.org/10.1007/s11009-007-9057-z.

    Article  Google Scholar 

  18. B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall, London (1986).

    MATH  Google Scholar 

  19. Z. I. Botev, J. F. Grotowski, and D. P. Kroese, Ann. Stat., 38, No. 5, 2916–2957 (2010), https://doi.org/10.1214/10-AOS799.

    Article  Google Scholar 

  20. A. V. Dobrovidov and I. M. Rudko, “Choosing the width of the window of the kernel function in the nonparametric estimation of the density derivative by the method of smoothed cross-validation,” Avtomat. Telemekh., No. 2, 42–58 (2010).

    Google Scholar 

  21. T. A. O’Brien, K. Kashinath, N. R. Cavanaugh, et al., Comp. Stat. Data Anal., 101, 148–160 (2016), https://doi.org/10.1016/j.csda.2016.02.014.

    Article  Google Scholar 

  22. S. Chen, J. Probab. Stat., 2015, 242683 (2015), https://doi.org/10.1155/2015/242683.

  23. D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley, New York (2015).

    MATH  Google Scholar 

  24. A. S. Sharakshane, I. G. Zheleznov, and V. A. Ivnitskii, Complex Systems, Vyssh. Shk., Moscow (1977).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

    A. V. Lapko & V. A. Lapko

  2. Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia

    A. V. Lapko, V. A. Lapko & A. V. Bakhtina

Authors
  1. A. V. Lapko
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  2. V. A. Lapko
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  3. A. V. Bakhtina
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Correspondence to A. V. Lapko.

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Translated from Izmeritel'naya Tekhnika, No. 1, pp. 17–22, January, 2022.

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Lapko, A.V., Lapko, V.A. & Bakhtina, A.V. Application of a Nonparametric Pattern Recognition Algorithm to the Problem of Testing the Hypothesis of the Independence of Variables of Multi-Valued Functions. Meas Tech 65, 17–23 (2022). https://doi.org/10.1007/s11018-022-02043-2

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  • DOI: https://doi.org/10.1007/s11018-022-02043-2

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