Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 519.2
SOME GENERALIZATIONS OF METHOD OF MOMENTS IN PROBABILITY DENSITY ESTIMATION BY ORTHOGONAL SERIES
V. V. Branishti
Reshetnev Siberian State Aerospace University 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation E-mail: branishti-v-v@yandex.ru
A problem of probability density function estimation for continuous random variable is considered in the paper. Actuality of this problem for science and technology including aerospace branch is discussed. Building of the probabil-ity density functions estimation by orthonormal series is considered. Applying of the method of moments to statistical estimating series coefficients is investigated, and some generalizations are suggested. Within the scope of method of moments the author uses consecutive ordinary moments of random variable. In this case the calculation of series coeffi-cients estimations is reduced to solving system of linear equations. The paper has the proof of the theorem that in specified conditions of orthonormal system choice, suggested gener-alization of the method of moments includes the ordinary method of moments and also more widespread estimating coefficients method by sample means of orthonormal functions as particular cases. The paper shows that in the case of using Legendre’s orthonormal system the considered methods are identical. The properties of built estimations are researched, mathematical expectations and covariance matrix are founded. The paper shows that in particular cases the estimations of series coefficients are biased. The estimations of series coefficients, which are calculated by suggested method, were used for building estimation of probability density function. The paper has results of numerical calcula-tions of quality functional values for built estimations of probability density function. The calculations are carried out for uniformly distributed random value. The author compares the suggested method with the widespread estimating method with using Chebyshev’s and trigonometric orthonormal systems. Research shows that generalized method of moments gives substantially better result on small samples.
Keywords: nonparametric indeterminacy, probability density function, statistical estimation, orthogonal functions, method of moments, matrix analysis.
References

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Branishti Vladislav Vladimirovich – senior lecturer, Higher mathematics Dept, Reshetnev Siberian State Aerospace University. Е-mail: branishti-v-v@yandex.ru.