Adaptive estimation of the sparsity in the Gaussian vector model

2017/03/01 by Carpentier, Alexandra, Verzelen, Nicolas
#62B10 #62C20 #62G10 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1703.00167

Abstract

Consider the Gaussian vector model with mean value θ. We study the twin problems of estimating the number |θ|₀ of non-zero components of θ and testing whether |θ|₀ is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of |θ|₀ as a multiple testing problem of all hypotheses |θ|₀ <= q, we both derive a new way of assessing the optimality of a sparsity estimator and we exhibit such an optimal procedure. This general approach provides a roadmap for estimating the complexity of the signal in various statistical models.

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• Adaptive robust estimation in sparse vector model
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