The Shannon information quantity in the tasks associated with linear regression: usage pattern
The article discusses the use of the Shannon information quantity (SIQ) in the tasks associated with linear regression. It has been 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 is equivalent to the use of the D-criterion in the problems of planning the experiment at a sufficiently large scale of parameters. The SIQ relatively constant regression parameters were determined. An alternative formulation of the optimal experiment planning (OEP) problem was considered and its relation to the traditional formulation was analyzed. The problem of information ordering of data using regression on the basis of principal components was considered. Some algorithms taking into account the value of information in the presence of partial data gaps were proposed.