ON THE USING OF THE SHANNON INFORMATION QUANTITY IN THE TASKS ASSOCIATED WITH LINEAR REGRESSION

Abstract

The article discusses the use of the Shannon information quantity (SIQ) in the tasks associated with linear regression. It is shown that the SIQ contained in the response components with respect to stochastic parameters is expressed through the Fisher information matrix, is a convex functional on the set of response components, and at a sufficiently large scale of parameters is equivalent to the use of the D-criterion in the problems of planning the experiment. Determined SIQ relatively constant regression parameters. An alternative formulation of the optimal experiment planning (OEP) problem is considered and its relation to the traditional formulation is analyzed. The problem of informative ordering of data using regression on the basis of principal components is considered. Algorithms that take into account the value of information in the presence of partial data gaps are proposed.

Keywords

• shannon information quantity
• linear regression
• stochastic regression parameter