An analysis of the ols estimates for the problem of parametric indentification of distributed dinamic processes in the situation of elimination of multicollinearity

Abstract

One of the most difficult problems of parametric identification is the estimation of the parameters of the models of distributed dynamic processes using statistical methods. It is known that one of the factors affecting the quality of the resulting model (for example, of regression), is multicollinearity. If the estimated regression model is intended to be used to study relationships (for example, economic relationships, etc.), then the elimination of multicollinear factors is mandatory, because their presence in the model can result in biased regression coefficients. The article suggests a method for reducing the dimensionality in order to eliminate multicollinearity in the problem of parametric identification of distributed dynamic processes. It also considers the possibility of using the Ordinary Least Squares (OLS) method for parametric identification of models of distributed dynamic processes in the case of biased estimates. We gave the name «alternative estimates» to the OLS estimates obtained as a result of the dimensionality reduction. It was then necessary to assess the effectiveness of the alternative estimates as compared to the normal OLS estimates. The study demonstrated that with a low level of observational errors (1 % or less), the use of direct OLS estimates for the identification of the parameters of distributed dynamic processes yields satisfactory results. At the same time, the displacement is always slightly greater than the standard deviation of the parameter estimate, which does not allow us to neglect this displacement, especially with high and average levels of observational errors. The use of alternative OLS estimates reduces the multicollinearity and, consequently, reduces the dimensionality of the problem. In the sample statistics and at any level of observational errors, the proposed method significantly reduces the standard error of parameter estimation.