Related papers: Wald tests of singular hypotheses
Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based…
The problem of characterizing a multivariate distribution of a random vector using examination of univariate combinations of vector components is an essential issue of multivariate analysis. The likelihood principle plays a prominent role…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly…
We study two functionals of a random matrix $\boldsymbol A$ with independent elements uniformly distributed over the cyclic group of integers $\{0,1,\ldots, M-1\}$ modulo $M$. One of them, $V_0(\boldsymbol A)$ with mean $\mu$, gives the…
The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute.…
We consider Wald type statistics designed for joint predictability and structural break testing based on the instrumentation method of Phillips and Magdalinos (2009). We show that under the assumption of nonstationary predictors: (i) the…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
We consider bivariate polynomials orthogonal on the bicircle with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…
We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution of the…
We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related, and in fact in competition, with the possibility of damping the…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
On a probability space $(\Omega, \mathcal F, \mathbb P)$ we consider two independent sequences $(a_k)_{k \geq 1}$ and $(b_k)_{k \geq 1}$ of i.i.d. random variables that are centered with unit variance and which admit a moment strictly…