Related papers: Optimal hypothesis testing for high dimensional co…

This paper proposes a new test for covariance matrices structure based on the correction to Rao's score test in large dimensional framework. By generalizing the CLT for the linear spectral statistics of large dimensional sample covariance…

The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $\epsilon$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS,…

Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…

We develop some graph-based tests for spherical symmetry of a multivariate distribution using a method based on data augmentation. These tests are constructed using a new notion of signs and ranks that are computed along a path obtained by…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Let $X$ be a centered random vector taking values in $\mathbb{R}^d$ and let $\Sigma= \mathbb{E}(X\otimes X)$ be its covariance matrix. We show that if $X$ satisfies an $L_4-L_2$ norm equivalence, there is a covariance estimator…

This paper proposes a max-test for testing (possibly infinitely) many zero parameter restrictions in an extremum estimation framework. The test statistic is formed by estimating key parameters one at a time based on many empirical loss…

Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…

Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given $n$ points $\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution where $X_i \in…

Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…

We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…

We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…

Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…

Given i.i.d. observations of a random vector $X \in \mathbb{R}^p$, we study the problem of estimating both its covariance matrix $\Sigma^*$, and its inverse covariance or concentration matrix {$\Theta^* = (\Sigma^*)^{-1}$.} We estimate…

We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional…

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…