Titlebook: Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference; Zheng Gao,Stilian Stoev Book 2021 The Author(s),

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爆米花

Risks, Procedures, and Error Models,ional setting. First, a general notion of statistical risk is formulated and used to provide a unified treatment of a variety of signal detection and support estimation problems considered in the literature. The relationship between various choices of risk functionals and their implications on the a

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surrogate

Bayes and Minimax Optimality, likelihood ratio thresholding procedures are always Bayes optimal. Consequently, the Oracle threshold estimation procedures are optimal for the class of log-concave error models and, otherwise, they are typically sub-optimal. These results lead to a slew of asymptotic minimax characterizations of t

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Uniform Relative Stability for Gaussian Arrays, arrays known as the uniform relative stability (URS) property. This property holds for a wide range of models. The purpose of this chapter is to provide a complete characterization of URS for Gaussian triangular arrays. The main result shows that the Gaussian arrays are URS if and only if they are

杀子女者

,Fundamental Statistical Limits in Genome-Wide Association Studies,WAS) aim to discover the set of gene variants associated with a disease. In the simple case of marginal association studies, one typically considers 2-by-2 contingency tables and computes non-central chi-square-type statistics (one for each genetic location), where the non-centrality parameter plays

heterodox

Time-Varying Discrete Linear Systems. 2 yields a variety of phase-transition results, many of which are new. The optimality and sub-optimality of some popular support estimation procedures are also established. The chapter provides a concise and yet complete account of the phase transitions in the context of sparse signal detection and support estimation in high dimensions.

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elucidate