Application of a nonparametric procedure for testing the hypothesis about the independence of random variables given a large amount of statistical data

• Published in: Measurement techniques Vol. 66; no. 10; pp. 744 - 754
• Main Authors: Lapko, A. V., Lapko, V. A., Bakhtina, A. V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2024; Springer; Springer Nature B.V
• Subjects: Algorithms; Analytical Chemistry; Characterization and Evaluation of Materials; Distribution (Probability theory); Forests; Hypotheses; Maximum likelihood method; Measurement Science and Instrumentation; Nonparametric statistics; Pattern recognition; Physical Chemistry; Physics; Physics and Astronomy; Probability density functions; Random variables; Remote sensing; Specific gravity; Statistical analysis; Hypothesis testing; Probability density; Forest areas; Regression estimate; 519.7 + 004.93; Pattern recognition; Independent random variables; Hypothesis; Remote sensing
• ISSN: 0543-1972; 1573-8906
• DOI: 10.1007/s11018-024-02288-z

The article considers a problem related to testing the hypothesis about the independence of random variables given large amounts of statistical data. The solution to this problem is necessary when estimating probability densities of random variables and synthesizing algorithms for processing information. A nonparametric procedure is proposed for testing the hypothesis about the independence of random variables in a sample containing a large amount of statistical data. The procedure involves the compression of initial statistical data by decomposing the range of values of random variables. The generated data array consists of the centers of sampling intervals and the corresponding frequencies of observations belonging to the original sample. The obtained data was used in the construction of a nonparametric pattern recognition algorithm, which corresponds to the maximum likelihood criterion. The distribution laws in the classes were evaluated assuming the independence and dependence of the compared random variables. When recovering the distribution laws of random variables in the classes, the regression estimates of probability densities were used. For these conditions, the probability of errors in recognizing patterns in the classes was estimated, and decisions about the independence or dependence of random variables were made according to their minimum value. The procedure was used in the analysis of remote sensing data on forest areas; linear and nonlinear relationships between the spectral features of the subject matter of the study were determined.