Analysis of the multicollinear econometric model parameters with a rank deficient observation matrix

Abstract

The topic of determining informative predictors, forming rational exogenous variables, substantiating the dimension and structure of predictor spaces is considered. The purpose of design and selection of characteristics is to prevent the effect of retraining, reduce the dimension in studying the processes apart from a master, build classifiers, reflect the process of dividing data into classes and determine the boundaries of solutions in limited space, as well as reasonable interpretation, provide in-depth understanding of the model and data for studying, visualization in spaces, the dimension of which is perceived by the researcher. The design predictor spaces and develop effective procedures problems for estimating the parameters of econometric models with multicollinear variables are developed. The study was made under alternative approaches to form the interdependencies models features. A mathematical toolkit is proposed for calculating the parameters of a linear econometric model in case of rank deficient observation matrix, based on the study of singular expansions. Using a singular toolkit for decomposing and analyzing the data matrix makes it possible to increase the operational efficiency and predictive quality of the procedures for estimating econometric models parameters. The mathematical approach to the construction of models of the interdependence of factors is intended to select characteristics and construct predictor spaces in the study of systems with multicollinear variables and rank deficient observation matrix.