A coverage theory for least squares. (18th November 2016) - Carè, Algo; Garatti, Simone; Campi, Marco C.
Summary: A sensible use of an estimation method requires that assessment criteria for the quality of the estimate be available. We present a coverage theory for the least squares estimate. By suitably modifying the empirical costs, one constructs statistics that are guaranteed to cover with known probability the cost associated with a next, still unseen, member of the population. All results of this paper are distribution free and can be applied to least squares problems in use across a variety of fields.