文章基本信息

标题：Hypothesis testing via affine detectors
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作者：Anatoli Juditsky ; Arkadi Nemirovski
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：2
页码：2204-2242
DOI：10.1214/16-EJS1170
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.