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Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and…
For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965, Kasiviswanathan et al, 2008) and the newer (non-symmetric) mechanisms…
This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the…
We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
There are many open questions pertaining to the statistical analysis of random objects, which are increasingly encountered. A major challenge is the absence of linear operations in such spaces. A basic statistical task is to quantify…
When working with textual data, a natural application of disentangled representations is fair classification where the goal is to make predictions without being biased (or influenced) by sensitive attributes that may be present in the data…
Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting…
In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit…
Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…