A coverage theory for least squares
Algo Carè, Simone Garatti, Marco C. Campi
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2017 · Volume 79 · Issue 5
Abstract
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.
Keywords
Coverage, Empirical distribution, Least squares, Order statistics, Statistics with distribution-free mean coverage
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