CONSISTENT APPLICATION OF PARAMETER ESTIMATION METHODS IN THE CONSTRUCTION OF REGRESSION MODELS
Authors:
1.
Irkutsk State University of Railway Transport
(Doctor of Technical Sciences, Professor; Professor of the Department of Information Systems and Information Security)
Irkutsk, Irkutsk region, Russian Federation
Irkutsk, Irkutsk region, Russian Federation
2.
Russian Federation
Type:
Article
Pages:
from 206
to 210
Status:
In work
Language:
Russian
Keywords:
REGRESSION MODEL, PARAMETER IDENTIFICATION, CONCESSION METHOD, LEAST ABSOLUTE VALUE AND ANTIROBUST ESTIMATION METHODS, LINEAR PROGRAMMING PROBLEM, CHEMICAL INDUSTRY
Abstract (English):
The paper provides a brief overview of publications on the application, due to various reasons of formal and (or) substantive nature, of several specialized methods, including those for estimating parameters, in developing a single regression model. In particular, the following are considered: a new modified two-parameter estimate of regression model parameters based on preliminary information for the parameter vector in order to circumvent the problem of multicollinearity; methods for estimating parameters of ordinary differential equations based on the local smoothing approach and the pseudo-least squares principle within the framework of measurement error in regression models; improved estimation strategies for the parameter matrix in multivariate multiple regression with general and natural linear constraints; a study of small sample properties for three different methods of estimating parameters of regression models with correlated binary responses; methodological and theoretical developments for models with variable coefficients. An algorithmic method for sequentially using several methods for estimating unknown parameters in the general case of a nonlinear regression model is developed, based on the application of the concession method, well known in decision theory. The basic condition for its use is the possibility of ordering identification methods (and, therefore, the corresponding loss functions) by preference, based on experience, knowledge, individual preferences of the researcher and the properties of the processed data sample. This method involves solving several optimization problems. When using the methods of least modules and anti-robust estimation, their consistent application leads to the need to solve two linear programming problems. Four versions of the linear regression model of development of the chemical industry of the Russian Federation are constructed. The volume of direct investments in the industry is used as the only independent variable.
The paper provides a brief overview of publications on the application, due to various reasons of formal and (or) substantive nature, of several specialized methods, including those for estimating parameters, in developing a single regression model. In particular, the following are considered: a new modified two-parameter estimate of regression model parameters based on preliminary information for the parameter vector in order to circumvent the problem of multicollinearity; methods for estimating parameters of ordinary differential equations based on the local smoothing approach and the pseudo-least squares principle within the framework of measurement error in regression models; improved estimation strategies for the parameter matrix in multivariate multiple regression with general and natural linear constraints; a study of small sample properties for three different methods of estimating parameters of regression models with correlated binary responses; methodological and theoretical developments for models with variable coefficients. An algorithmic method for sequentially using several methods for estimating unknown parameters in the general case of a nonlinear regression model is developed, based on the application of the concession method, well known in decision theory. The basic condition for its use is the possibility of ordering identification methods (and, therefore, the corresponding loss functions) by preference, based on experience, knowledge, individual preferences of the researcher and the properties of the processed data sample. This method involves solving several optimization problems. When using the methods of least modules and anti-robust estimation, their consistent application leads to the need to solve two linear programming problems. Four versions of the linear regression model of development of the chemical industry of the Russian Federation are constructed. The volume of direct investments in the industry is used as the only independent variable.
Keywords:
REGRESSION MODEL, PARAMETER IDENTIFICATION, CONCESSION METHOD, LEAST ABSOLUTE VALUE AND ANTIROBUST ESTIMATION METHODS, LINEAR PROGRAMMING PROBLEM, CHEMICAL INDUSTRY
REGRESSION MODEL, PARAMETER IDENTIFICATION, CONCESSION METHOD, LEAST ABSOLUTE VALUE AND ANTIROBUST ESTIMATION METHODS, LINEAR PROGRAMMING PROBLEM, CHEMICAL INDUSTRY
