Related papers: High-dimensional tests for spherical location and …
We prove a weak form of the soliton resolution conjecture of bounded solutions of high-dimensional fourth-order Schrodinger equations. The result relies upon two properties to be proved: the asymptotic frequency localization and the…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…
Testing heteroscedasticity of the errors is a major challenge in high-dimensional regressions where the number of covariates is large compared to the sample size. Traditional procedures such as the White and the Breusch-Pagan tests…
Existing methods for high-dimensional changepoint detection and localization typically focus on changes in either the mean vector or the covariance matrix separately. This separation reduces detection power and localization accuracy when…
A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or…
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different…
The sign test (Arbuthnott, 1710) and the Wilcoxon signed-rank test (Wilcoxon, 1945) are among the first examples of a nonparametric test. These procedures -- based on signs, (absolute) ranks and signed-ranks -- yield distribution-free tests…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…