About the full prediction approximation by a lot of partial predictions in case of incomplete data

Abstract

In this article, we are talking about the random subspaces method in forecasting under the condition of incomplete data and about estimation of a full forecast based on a set of partial predictions. Centered partial predictions are considered without loss of generality. According to the statistical model, off-diagonal elements in the correlation matrix of partial predictions are considered random with known mathematical expectation and variance. In case of this random matrix, analytical expressions are obtained for the mathematical expectation of the determinant and minors. Based on these results, a class of more accurate estimates of the full prediction is constructed, which differ from the mean partial prediction by a multipliers that depend on the statistical parameters of the correlation matrix of partial predictions. The results of modeling and practical forecasting based on incomplete biogeographic data are presented.