Corpus ID: 222177369

High dimensional asymptotics of likelihood ratio tests in Gaussian sequence model under convex constraint

  title={High dimensional asymptotics of likelihood ratio tests in Gaussian sequence model under convex constraint},
  author={Qiyang Han and Bodhisattva Sen and Yandi Shen},
  journal={arXiv: Statistics Theory},
In the Gaussian sequence model $Y=\mu+\xi$, we study the likelihood ratio test (LRT) for testing $H_0: \mu=\mu_0$ versus $H_1: \mu \in K$, where $\mu_0 \in K$, and $K$ is a closed convex set in $\mathbb{R}^n$. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair $(\mu_0,K)$, in the high dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense… Expand

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