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In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering. Thus, we convert almost all(More)
In this paper, we improve known results on the convergence rates of spectral distributions of large dimensional sample covariance matrices of size p n. Depending on the limiting value y of the ratio p=n and by using the tool of Stieltjes transforms, we first prove that the expected spectral distribution converges to the limiting Marčenko-Pastur distribution(More)
For adaptive clinical trials using a generalized Friedman's urn design, we derive the limiting distribution of the urn composition under staggered entry and delayed response. The stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient's response. A very general setup is employed with K treatments and L responses. When(More)
is the square root of a nonnega-tive definite matrix Tn and Xn is the n × N matrix of the upper-left corner of the double array. The matrix An can be considered as a sample covariance matrix of an i.i.d. sample from a population with mean zero and covariance matrix Tn, or as a multivariate F matrix if Tn is the inverse of another sample covariance matrix.(More)
Let S n = 1 n X n X * n where X n = {X ij } is a p × n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Y n (t 1 , t 2 , σ) = √ p(x n (t 1) * (S n + σ I) −1 x n (t 2) − x n (t 1) * x n (t 2)m n (σ)) in which σ > 0 and m n (σ) = dF yn (x) x+σ where F y n (x) is the Marčenko–Pastur law with parameter y n = p/n; which converges(More)
Random matrix theory is used to derive the limit and asymptotic distribution of signal-to-interference-plus-noise ratio (SIR) for a class of suboptimal minimum mean-square-error (MMSE) receivers applied to large random systems with unequal-power users. We prove that the limiting SIR converges to a deterministic value when K and N go to infinity with lim K/N(More)
We consider the problem of model (or variable) selection in the classical regression model using the GIC (general information criterion). In this method the maximum likelihood is used with a penalty function denoted by Cn, depending on the sample size n and chosen to ensure consistency in the selection of the true model. There are various choices of Cn(More)
In this paper, a general form of M-estimation is proposed and some asymptotics are investigated. The model covers all linear and nonlinear regression models, AR time series, EIVR models, etc. as its special cases. The dispersion functions may be convex or differences of convex functions, the later covers almost all useful choices of the dispersion(More)
For n i.i.d. uniform points in [0, 1] d , d ≥ 2, let L n be the total distance from the origin to all the minimal points under the coordinate-wise partial order (this is also the total length of rooted edges of a minimal directed spanning tree on the given n random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of L n , and(More)