Department of Mathematics - Seminar on Statistics - High dimensional asymptotics of likelihood ratio tests in the Gaussian sequence model under convex constraints

10:00am - 11:00am (Passcode: 690595)

In the Gaussian sequence model Y= μ+ ξ, we study the likelihood ratio test (LRT) for testing H0 :μ= μ0 versus H1 :μ∈K, where μ0∈K, and K is a closed convex set in Rn. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (μ0, 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 non-uniform with respect to the Euclidean metric, and illustrate the conservative nature of existing minimax optimality and sub-optimality results for the LRT. A variety of examples, including testing in the orthant/circular cone, isotonic regression, Lasso, and testing parametric assumptions versus shape-constrained alternatives, are worked out to demonstrate the versatility of the developed theory.


This talk is based on joint work with Yandi Shen(UW, Chicago) and Bodhisattva Sen(Columbia).

Event Format
Speakers / Performers:
Prof. Qiyang HAN
Rutgers University
Recommended For
Faculty and staff
PG students
UG students
Department of Mathematics
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