HIGH TECH IN EARTH SPACE RESEARCH

Nonlinear estimation steamy one-parameter regression in terms of lack of statistics

Getmanskaya I.V.

Parametric regression is a mathematical model of a phenomenon in the form of functional dependence between the parameters of this phenomenon, one of which is a dependent variable and independent arguments of a function, and the other is its unknown estimated parameters.

Since measurements are often burdened with errors, the construction of the model is carried out in the probabilistic scheme of the problem statement, and the estimates of unknown parameters are carried out by statistical methods using evaluation equations. For a nonlinear regression that is not intrinsically linear, the estimated equations with respect to the estimated parameter are not analytically solved. In this case, iteration methods are used, the effectiveness of which depends on the initial approximation.   There is an iterative formula for generalized minimal-contrast estimation of non-linear one-parameter pair (one argument) regression. Its components are the implementations of the estimated regression parameter found analytically or numerically by the regression function at measured values of the dependent variable and the independent argument without taking into account the measurement errors. The average of these realizations with a certain approximation accuracy is a consistent estimate, which was previously proved by the numerical characteristics of the realizations found. This estimate can be used as an initial estimate in an iterative parametric regression estimation formula.

In this paper, the implementation of the estimated parameter with approximately zero variance is considered not only as an initial approximation, but also as a self-sufficient estimate, if its accuracy is satisfactory. It is an approximation of the estimated parameter of known accuracy proportional to the cube of the standard deviation of the initial data.

The results of the simulation experiment for estimating regression parameters by the proposed approximation method and by means of a consistent assessment are consistent with the theoretical descriptions of the methods. Their comparison is in favor of approximation, if the volume of the original data is less than ten. In this case, the deviation from the true value of the estimated parameter is less than the deviation of the compared state estimate by a maximum of two orders of magnitude (188 times) by at least 1.5 times.

Conditions of optimality of the method assumes its use in studies of rare phenomena, as well as in expensive experiments in the broad (economic and humanitarian) sense of the word, 

The effectiveness of the evaluation method can be anticipated by checking to experience the fulfillment of the conditions of evaluation formation, which depend on the range of values of the argument of the regression function.

Editorial board

Bobrowsky V.I.
(Ph.D., Associate Professor, Head of Department of "INTELTEH")

Borisov V.V.
(Ph.D., Professor, Actual Member of the Academy of Military Sciences, Professor, Department of Computer Science of MPEI)

Budko P.A.
(Ph.D., Professor, Department of Technical communication and automation in S.M. Budjonny Military Academy of the Signal Corps)

Budnikov S.A.
(Ph.D., associate professor, Actual Member of the Academy of Education Informatization, Head of the automated control systems Department in Russian Air Force Military Educational and Scientific Center “Air Force Academy named after Professor N.E. Zhukovsky and Y.A. Gagarin”)

Verhova G.V.
(Ph.D., Professor, Head of Department of Automation communication companies In the Bonch-Bruevich Saint Petersburg State University of Telecommunications)

Goncharevsky V.S.
(Ph.D., Professor, Honored Worker of Science and Technology of the Russian Federation, Professor of technologies and technical support and maintenance of the automated control systems in Military Space Academy of A.F. Mozhaysky)

Komashinskiy V.I.
(Ph.D., Professor, professor of processing and transmission discrete messages in the Bonch-Bruevich Saint Petersburg State University of Telecommunications)

Kirpanev A.V.
(Ph.D., Associate Professor, Head of JSC "Scientific Production Enterprise "Radar MMS")

Kurnosov V.I.
(Ph.D., Professor, Academician of Academy of Sciences of the Arctic, Academician of the International Academy of Informatization, International Academy of defense, security, law and order, corresponding member of the Academy of Natural Sciences, Senior Researcher" Open Joint Stock Company "Scientific Research Institute "Rubin")

Manuilov Y.S.
(Ph.D., Professor, Department of automated control systems space complexes in Military Space Academy of A.F. Mozhaysky)

Morozov A.V.
(Ph.D., Professor, Actual Member of the Academy of Military Sciences, Head of the Department of automated command and control systems in Military Аcademy of troops of antiaircraft defense)

Moshak N.N.
(Ph.D., Associate Professor, head of the department of "INTELTEH")

Prorok V.Y.
(Ph.D., Professor, professor of automatic control systems in Military Space Academy of A.F. Mozhaysky)

Semenov S.S.
(Ph.D., associate professor, professor of technical communication and automation in S.M. Budjonny Military Academy of the Signal Corps)

Sinicyn E.A.
(Ph.D., Professor, Head of the Research Department of JSC "The All-Russian research institute of radio equipment")

Shatrakov Y.G.
(Ph.D., Professor, Honored Worker of Science, Scientific Secretary of JSC "The All-Russian research institute of radio equipment")