Electronic Journal of Statistics

Hypothesis testing via affine detectors

Anatoli Juditsky and Arkadi Nemirovski

Full-text: Open access

Abstract

In this paper, we further develop the approach, originating in [13], to “computation-friendly” hypothesis testing via Convex Programming. Most of the existing results on hypothesis testing aim to quantify in a closed analytic form separation between sets of distributions allowing for reliable decision in precisely stated observation models. In contrast to this descriptive (and highly instructive) traditional framework, the approach we promote here can be qualified as operational – the testing routines and their risks are yielded by an efficient computation. All we know in advance is that, under favorable circumstances, specified in [13], the risk of such test, whether high or low, is provably near-optimal under the circumstances. As a compensation for the lack of “explanatory power,” this approach is applicable to a much wider family of observation schemes and hypotheses to be tested than those where “closed form descriptive analysis” is possible.

In the present paper our primary emphasis is on computation: we make a step further in extending the principal tool developed in [13] – testing routines based on affine detectors – to a large variety of testing problems. The price of this development is the loss of blanket near-optimality of the proposed procedures (though it is still preserved in the observation schemes studied in [13], which now become particular cases of the general setting considered here).

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 2204-2242.

Dates
Received: July 2016
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1468954728

Digital Object Identifier
doi:10.1214/16-EJS1170

Mathematical Reviews number (MathSciNet)
MR3528713

Zentralblatt MATH identifier
1345.62077

Subjects
Primary: 62G10: Hypothesis testing 62C20: Minimax procedures
Secondary: 62M02: Markov processes: hypothesis testing 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 90C25: Convex programming 65K10: Optimization and variational techniques [See also 49Mxx, 93B40]

Keywords
Hypothesis testing nonparametric testing composite hypothesis testing statistical applications of convex optimization

Citation

Juditsky, Anatoli; Nemirovski, Arkadi. Hypothesis testing via affine detectors. Electron. J. Statist. 10 (2016), no. 2, 2204--2242. doi:10.1214/16-EJS1170. https://projecteuclid.org/euclid.ejs/1468954728


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