Global Non-asymptotic Confidence Sets for General Linear Models

In this paper we consider the problem of constructing confidence sets for the parameters of general linear models. Based on subsampling techniques and building on earlier exact finite sample results due to Hartigan, we compute the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence set containing the true parameters with guaranteed probability is obtained. All results hold rigorously true for any finite number of data points and no asymptotic theory is involved. Moreover, prior knowledge on the uncertainty affecting the data is reduced to a minimum. The approach is illustrated on a simulation example, showing that it delivers practically useful confidence sets with guaranteed probabilities. Copyright c ©2005 IFAC.