Global non-asymptotic confidence sets for general linear models

In this paper we consider the problem ofconstructing confidence sets for the parameters of general linearmodels. Based on subsampling techniques and building on earlierexact finite sample results due to Hartigan, we compute the exactprobability that the true parameters belong to certain regions inthe parameter space. By intersecting these regions, a confidenceset containing the true parameters with guaranteed probability isobtained. All results hold rigorously true for any finite numberof data points and no asymptotic theory is involved. Moreover,prior knowledge on the uncertainty affecting the data is reducedto a minimum. The approach is illustrated on a simulation example,showing that it delivers practically useful confidence sets withguaranteed probabilities.