It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko–Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the...

In the spiked population model introduced by Johnstone (2001) [11], the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein...

Let (εj)j≥0 be a sequence of independent p-dimensional random vectors and τ≥1 a given integer. From a sample ε1,…,εT+τ of the sequence, the so-called lag-τ auto-covariance matrix is Cτ=T−1∑j=1Tετ+jεjt. When the dimension p is large compared to the sample size T, this paper...

Let X1,…,Xn1+1∼iidNp(μ1,Σ1) and Y1,…,Yn2+1∼iidNp(μ2,Σ2) be two independent random samples, where pn2. In this article, we propose a new test for the proportionality of two large p×p covariance matrices Σ1 and Σ2. By applying modern random matrix theory, we establish the asymptotic...

We are concerned with the behavior of the eigenvalues of renormalized sample covariance matrices of the form Cn=np(1nAp1/2XnBnXn∗Ap1/2−1ntr(Bn)Ap) as p,n→∞ and p/n→0, where Xn is a p×n matrix with i.i.d. real or complex valued entries Xij satisfying E(Xij)=0, E|Xij|2=1 and having...

We consider the moment space MnK corresponding to p×p complex matrix measures defined on K (K=[0,1] or K=T). We endow this set with the uniform distribution. We are mainly interested in large deviation principles (LDPs) when n→∞. First we fix an integer k and study the vector of the first k...

In this paper we define distributions on the moment spaces corresponding to p×p real or complex matrix measures on the real line with an unbounded support. For random vectors on the unbounded matricial moment spaces we prove the convergence in distribution to the Gaussian orthogonal ensemble or...

We study the problem of ergodicity, stationarity and maximum likelihood estimation for multinomial logistic models that include a latent process. Our work includes various models that have been proposed for the analysis of binary and, more general, categorical time series. We give verifiable...

Empirical and sequential empirical copula processes play a central role for statistical inference on copulas. However, as pointed out by Johan Segers [J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (3) (2012) 764–782] the usual...

We derive the asymptotical distributions of two-sample U-statistics and two-sample empirical U-quantiles in the case of weakly dependent data. Our results apply to observations that can be represented as functionals of absolutely regular processes, including e.g. many classical time series...