Key words
minimax, no smooth analysis, estimation, approximation, algorithm, econometric modeling, multiple regression model, rectangular grid.
articles
The author:
Vygodchikova I. Published in
№ 4(58)
28 august 2015 year
Rubric: Mathematical tools
Rubric: Mathematical tools
Estimating the parameters of a multiple linear regression model according to the minimax criterion
In the study of dynamic processes is necessary realistic and objective causal analysis of events.
Such analysis is possible due to application of mathematical and computer simulation methods. Existing
methods of modelling, quantification and forecasting typically require large volume of the original
data, which is not always available, especially when the simulated indicator depends on several
variables, and they underestimate the possibility of extremely rare events that violate distribution pattern
of this indicator. The purpose of this paper — development of a new minimax method estimating
of dynamic patterns for rectangular grid of values of independent variables, mathematical study
of a new method of modeling, the establishment of an effective algorithm, demonstration of application.
Are stated and proved the properties of the solution of the problem which is implementation of
tools modeling technique, that allowed develop an algorithm in the form of step by step instructions,
which is easily implemented in any software environment. In the article demonstrated examples of
implementation of the algorithm, in particular, reviewed its application to assess the dynamic trends
for the purpose of data compression and prediction of missing values in the sample. Proposed a minimax
model of multiple regression and its realization for estimation of parameters of autoregressive
depending. Mathematical justification and obtained the properties of the new model allowed to develop
effective, from the viewpoint of availability of the software implementation in real-time, algorithm.
The author:
Vygodchikova I.
Degree:
PhD in Physics & Mathematics, Associate Professor, National Research Saratov State University named after N. G. Chernyshevsky
Location:
Saratov
