A coverage theory for least squares

• 成果类型: Article
• 署名作者: Care, Algo; Garatti, Simone; Campi, Marco C.
• 署名单位: HUN-REN; HUN-REN Institute for Computer Science & Control; Polytechnic University of Milan; University of Brescia
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12219
• 发表日期: 2017
• 页码: 1367-1389
• 关键词: Post-selection Inference; randomized solutions; optimization; feasibility; INEQUALITY; regression

摘要

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.