Statistical inference for the optimal approximating model

Rohde, Angelika; Dümbgen, Lutz (2013). Statistical inference for the optimal approximating model. Probability theory and related fields, 155(3-4), pp. 839-865. Springer 10.1007/s00440-012-0414-7

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In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Rohde, Angelika and Dümbgen, Lutz

Subjects:

500 Science > 510 Mathematics

ISSN:

0178-8051

Publisher:

Springer

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

01 Apr 2014 02:37

Last Modified:

22 Oct 2019 18:11

Publisher DOI:

10.1007/s00440-012-0414-7

BORIS DOI:

10.7892/boris.41523

URI:

https://boris.unibe.ch/id/eprint/41523

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