A coverage theory for least squares. (18th November 2016)

• Record Type: Journal Article
• Authors: Carè, Algo; Garatti, Simone; Campi, Marco C.
• Is Part Of: Journal of the Royal Statistical Society. Volume 79:Number 5(2017)
• Page Start: 1367
• Page End: 1389
• Publication Date: 2016-11-18
• Subjects: Coverage -- Empirical distribution -- Least squares -- Order statistics -- Statistics with distribution‐free mean coverage; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12219
• Languages: English
• ISSNs: 1369-7412

Abstract

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.