Prediction of Estimates' Accuracy for Linear Regression with a Small Sample Size

Abstract

We consider the problem of linear regression in the case of an extremely small sample size. It is difficult to obtain good estimates of model parameters and confidence interval in this case. We develop an approach based on the conformity estimation principle. Within this approach we form a set of subsystems with square matrixes and calculate a set of estimates for them. Then we choose a subsystem from initial system for which these estimates mutually the closest (function of mutual proximity is minimum). Then, we calculate a final estimate on this subsystem. We also used the mutual conformity function to predict the estimate's accuracy. Our approach is based on the assumption that there is a relationship between the estimation errors and values of the mutual conformity function. That is a new view on the problem of small sample size confidence intervals.