Comparison between two types of large sample covariance matrices
نویسندگان
چکیده
منابع مشابه
Comparison between two types of large sample covariance matrices
Let {X ij }, i, j = · · · , be a double array of independent and identically distributed (i.i.d.) real random variables with EX 11 = µ, E|X 11 − µ| 2 = 1 and E|X 11 | 4 < ∞. Consider sample covariance matrices (with/without empirical centering) S = 1 n n j=1 (s j − ¯ s)(s j − ¯ s) T and S = 1 n n j=1 s j s T j , where ¯ s = 1 n n j=1 s j and s j = T 1/2 n (X 1j , · · · , X pj) T with (T 1/2 n) ...
متن کاملExact Separation of Eigenvalues of Large Dimensional Sample Covariance Matrices
Let B n = (1/N)T 1/2 n is a Hermitian square root of the nonnegative definite Hermitian matrix T n. It is shown in Bai and Silverstein (1998) that, under certain conditions on the eigenvalues of T n , with probability one no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large n. For these n the interval corresponds t...
متن کاملEigenvalue Distribution of Large Sample Covariance Matrices of Linear Processes
We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable i = 1, . . . , p is modelled as a linear process (Xi,t)t=1,...,n = ( ∑∞ j=0 cjZi,t−j)t=1,...,n, where {Zi,t} are assumed to be independent random variables with finite fourth moments. If the sample size n and the number of variabl...
متن کاملConvergence Rates of Spectral Distributions of Large Sample Covariance Matrices
In this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p× n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marčenko–Pastur distribution with the dimension sample size ratio y = yn = p/n at a rate of O(n−1/2) if y keeps away from 0 and 1, u...
متن کاملEigenvalues of Large Sample Covariance Matrices of Spiked Population Models
We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits for a general class of samples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2014
ISSN: 0246-0203
DOI: 10.1214/12-aihp506