THE METHOD OF STATISTICAL MOMENTS IN A POLYNOMIAL REGRESSION OF CORRELATION DEPENDENCE
Article Sidebar
Main Article Content
Abstract
The methods of probability theory substantiate a brief procedure that allows us to express the parameters of the polynomial regression of conditional mathematical expectation through mixed statistical moments of a system of random variables. Examples of linear and quadratic regression are implemented. In the second case, consideration is limited to the situation when the probability density of a random argument is an even function. The result was obtained without cumbersome calculations, since it was obtained using not the initial statistical moments resulting from the least squares method, but mixed central moments reflecting the type of regression curve. It is shown that in the general case, taking into account the nonlinearity of the correlation dependence only strengthens the inequality, which is the criterion for the adequacy of the regression approximation. The convergence of such a procedure is confirmed if the conditional expectation is not essentially a polynomial.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Gmurman, V. E. (1972) Teoriya veroyatnostei i matematicheskaya statistika [Theory of Probability and Mathematical Statistics]. Moscow: Vysshaya shkola. (In Russ.).
Kovalenko, I. N., & Filippova, A. A. (1973). Teoriya veroyatnostei i matematicheskaya statistika [Theory of Probability and Mathematical Statistics]. Moscow: Vysshaya shkola. (In Russ.).
Pyt'ev, Yu. P., & Shishmarev. I. A. (1983). Kurs teorii veroyatnostei i matematicheskoi statistiki dlya fizikov [Course of Probability Theory and Mathematical Statistics for Physicists]. Moscow: Publ. Mosk. un-ta. (In Russ.).
Ekhilevskiy, S. G., Golubeva, O. V., Zabelendik, O. N., & Struk, T. S. (2019) Contribution of excesses of the gamma distribution to the asymptotics of factorials with large arguments. System analysis and information Technology, 1(15) – 2(16), 119–125.
Ekhilevskiy, S. G., Golubeva, O. V., & Potapenko, E. P. (2020). Teoretiko-veroyatnostnyi podkhod k modelirovaniyu respiratora na khimicheski svyazannom kislorode. Bezopasnost' truda v promyshlennosti [Labor safety in industry], (10), 7–15. (In Russ.).
Ekhilevskiy, S. G., Golubeva, O. V., Potapenko, E. P., & Rud'kova, T. S. (2016) Nezavisimye povtornye ispytaniya kak asimptoticheski gaussovskii sluchainyi protsess [Independent Retests as an Asymptotically Gaussian Stochastic Process]. Vestnik Polotskogo gosudarstvennogo universiteta. Seriya C, Fundamental'nye nauki [Herald of Polotsk State University. Series С. Fundamental sciences], (2), 111–116.