Minimax Euclidean Separation Rates for Testing Convex Hypotheses in ℝ^d

2017/02/13 by Gilles Blanchard, Blanchard, Gilles, Alexandra Carpentier +3
Computer Science · Mathematics · #62G10 #FOS: Mathematics #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G10 #stat.TH

paper · pdf · doi:10.48550/arxiv.1702.03760

openalex publication_date 2017/02/13 · arxiv created 2018/08/23 · arxiv updated 2018/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset C of ℝ^d. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension d and the sample size/variance parameter n giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non- smooth choices for C.

Citations

• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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