A Mathematical-Statistics Approach to the Least Squares Method

Abstract

We consider a mathematical-statistics approach to least-squares parameter estimation in a linear multiple regression model. This approach has led to a detailed description of the basic premises for the emergence and application of the least-squares method, produced a number of general distributional and statistical formulas for the estimation of model parameters independently of a specific joint distribution of the random variables, provided a deeper understanding of the parameter estimation risks associated with model specification errors, and made it possible to identify the place and role of knowledge of the theoretical and empirical distributions of observation errors.