Corpus ID: 222177369

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

@article{Han2020HighDA,
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},
year={2020}
}
• Published 2020
• Mathematics
• 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

References

SHOWING 1-10 OF 85 REFERENCES
A general method for power analysis in testing high dimensional covariance matrices
• Mathematics
• 2021
Covariance matrix testing for high dimensional data is a fundamental problem. A large class of covariance test statistics based on certain averaged spectral statistics of the sample covariance matrixExpand
Second-order Stein: SURE for SURE and other applications in high-dimensional inference
• Mathematics
• The Annals of Statistics
• 2021
Stein's formula states that a random variable of the form $z^\top f(z) - {\rm{div}} f(z)$ is mean-zero for all functions $f$ with integrable gradient. Here, ${\rm{div}} f$ is the divergence of theExpand
Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
• Mathematics
• 2020
The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families ofExpand
Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance.
• Mathematics
• 2020
We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that theExpand
On a phase transition in general order spline regression
• Mathematics
• 2020
In the Gaussian sequence model $Y= \theta_0 + \varepsilon$ in $\mathbb{R}^n$, we study the fundamental limit of approximating the signal $\theta_0$ by a class $\Theta(d,d_0,k)$ of (generalized)Expand
Isotonic regression in general dimensions
• Mathematics
• The Annals of Statistics
• 2019
We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed,Expand
Limit distribution theory for block estimators in multiple isotonic regression
• Mathematics
• 2019
We study limit distributions for the tuning-free max-min block estimator originally proposed in [FLN17] in the problem of multiple isotonic regression, under both fixed lattice design and randomExpand
Minimax Rate of Testing in Sparse Linear Regression
• Mathematics, Computer Science
• Autom. Remote. Control.
• 2019
It is shown that, in Gaussian linear regression model with p < n, where p is the dimension of the parameter and n is the sample size, the non-asymptotic minimax rate of testing has the form sqrt((s/n) log(1 + sqrt(p)/s)). Expand
Samworth, Isotonic regression in general dimensions
• Ann. Statist
• 2019
The geometry of hypothesis testing over convex cones: Generalized likelihood tests and minimax radii
• Computer Science, Mathematics
• The Annals of Statistics
• 2019
This work provides a sharp characterization of the GLRT testing radius up to a universal multiplicative constant in terms of the geometric structure of the underlying convex cones, and proves information-theoretic lower bounds for minimax testing radius again in Terms of geometric quantities. Expand