
Hypothesis Testing for HighDimensional Multinomials: A Selective Review
The statistical analysis of discrete data has been the subject of extens...
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Testing the Number of Regimes in Markov Regime Switching Models
Markov regime switching models have been used in numerous empirical stud...
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Superconsistency of tests in high dimensions
To assess whether there is some signal in a big database, aggregate test...
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Optimality of the max test for detecting sparse signals with Gaussian or heavier tail
A fundamental problem in highdimensional testing is that of global null...
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Signal detection via Phidivergences for general mixtures
In this paper we are interested in testing whether there are any signals...
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Twosample testing in nonsparse highdimensional linear models
In analyzing highdimensional models, sparsity of the model parameter is...
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Isotonic regression for metallic microstructure data: estimation and testing under order restrictions
Investigating the main determinants of the mechanical performance of met...
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High dimensional asymptotics of likelihood ratio tests in Gaussian sequence model under convex constraint
In the Gaussian sequence model Y=μ+ξ, we study the likelihood ratio test (LRT) for testing H_0: μ=μ_0 versus H_1: μ∈ K, where μ_0 ∈ K, and K is a closed convex set in ℝ^n. In particular, we show that under the null hypothesis, normal approximation holds for the loglikelihood ratio statistic for a general pair (μ_0,K), in the high dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense. The normal approximation further leads to a precise characterization of the power behavior of the LRT in the high dimensional regime. These characterizations show that the power behavior of the LRT is in general nonuniform with respect to the Euclidean metric, and illustrate the conservative nature of existing minimax optimality and suboptimality results for the LRT. A variety of examples, including testing in the orthant/circular cone, isotonic regression, Lasso, and testing parametric assumptions versus shapeconstrained alternatives, are worked out to demonstrate the versatility of the developed theory.
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