Limit Theorems for Large Dimensional Sample Means , Sample Covariance Matrices and Hotelling ’ S T 2 Statistics
نویسندگان
چکیده
In this paper, we prove the central limit theorem for Hotelling’s T 2 statistics when the dimension of the random vectors is proportional to the sample size via investigating asymptotic independence and random quadratic forms involving sample means and sample covariance matrices.
منابع مشابه
Statistic under Large Dimension
Sample covariance matrices are also of essential importance in multivariate statistical analysis because many test statistics involve their eigenvalues and/or eigenvectors. The typical example is T 2 statistic, which was proposed by Hotelling [2]. We refer to [1] and [3] for various uses of the T 2 statistic. The T 2 statistic, which is the origin of multivariate linear hypothesis tests and the...
متن کاملAsymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles
We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the number of variates and Xn,r such a matrix, a generalization of the Bartlett-type theorems gives a decomposi...
متن کاملComparison 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 کاملJackknife Empirical Likelihood Test for Equality of Two High Dimensional Means
There is a long history of testing the equality of two multivariate means. A popular test is the Hotelling T , but in large dimensions it performs poorly due to the possible inconsistency of sample covariance estimation. Bai and Saranadasa (1996) and Chen and Qin (2010) proposed tests not involving the sample covariance, and derived asymptotic limits, which depend on whether the dimension is fi...
متن کاملCorrections to LRT on Large Dimensional Covariance Matrix by RMT
Abstract: In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension is large compared to the sample size. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008