Bootstrap tests for unbiasedness of predictors

Abstract

In this paper, the analysis is focused on the unbiasedness of prediction based on a linear regression model. The accuracy of the considered predictors is measured by means of a statistical test based on the ex-post prediction variance. A significantly large value of the ratio of ex-post prediction variances and residual variance leads to the rejection of the hypothesis on unbiasedness of prediction. The distribution of the ratio is assessed by means of the parametric bootstrap procedure. Moreover, bootstrap-type tests, attempting to verify the unbiasedness of three predictors of the linear regression, are proposed. The distribution of the linear regression error term is assumed to be normal or t-Student. The power of considered statistical tests is examined based on an extensive simulation analysis.