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

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...

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Veröffentlicht in:	Measurement techniques Jg. 65; H. 1; S. 17 - 23
Hauptverfasser:	Lapko, A. V., Lapko, V. A., Bakhtina, A. V.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.04.2022 Springer Springer Nature B.V
Schlagworte:	Algorithms Analytical Chemistry Characterization and Evaluation of Materials Hypotheses Measurement Science and Instrumentation Nonparametric statistics Object recognition Pattern recognition Physical Chemistry Physics Physics and Astronomy Random noise Random variables Remote sensing Two dimensional analysis maximum likelihood test kernel estimation of probability density hypothesis testing multi-valued functional dependencies dependent random variables two-dimensional random variables independent random variables pattern recognition algorithm
ISSN:	0543-1972, 1573-8906
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Abstract	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.
AbstractList	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.
Audience	Academic
Author	Lapko, A. V. Bakhtina, A. V. Lapko, V. A.
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Shk – reference: ScottDWMultivariate Density Estimation: Theory, Practice, and Visualization2015New YorkWiley1311.62004 – reference: DuttaSComm. Stat.-Simul. Comp.201645247249010.1080/03610918.2013.862275 – reference: HallPAnn. Stat.19831141156117410.1214/aos/1176346329 – reference: JiangMProvostSBJ. Stat. Comp. Simul.201484361462710.1080/009 – reference: 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. – reference: 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. – reference: BotevZIKroeseDPMethod. Comp. Appl. Probab.200810343545110.1007/s11009-007-9057-z – reference: BowmanAWJ. Stat. Comp. Simul.19852131332710.1080/00949658508810822 – reference: BotevZIGrotowskiJFKroeseDPAnn. Stat.20103852916295710.1214/10-AOS799 – reference: LapkoAVLapkoVAAnalysis of methods for optimizing nonparametric estimation of the probability density using a kernel function blur coefficientIzmer. Tekhn., No.2017638 – reference: SilvermanBWDensity Estimation for Statistics and Data Analysis1986LondonChapman & Hall0617.62042 – volume: 6 start-page: 3 year: 2017 ident: 2043_CR15 publication-title: Izmer. Tekhn., No. – volume-title: Density Estimation for Statistics and Data Analysis year: 1986 ident: 2043_CR18 – volume-title: Probability Theory and Mathematical Statistics: Textbook year: 2018 ident: 2043_CR2 – ident: 2043_CR22 doi: 10.1155/2015/242683 – volume: 21 start-page: 313 year: 1985 ident: 2043_CR9 publication-title: J. Stat. Comp. 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SubjectTerms	Algorithms Analytical Chemistry Characterization and Evaluation of Materials Hypotheses Measurement Science and Instrumentation Nonparametric statistics Object recognition Pattern recognition Physical Chemistry Physics Physics and Astronomy Random noise Random variables Remote sensing Two dimensional analysis
Title	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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