Eigenvectors of some large sample covariance matrix ensembles
نویسندگان
چکیده
منابع مشابه
On Asymptotics of Eigenvectors of Large Sample Covariance Matrix
Let {Xij}, i, j = . . . , be a double array of i.i.d. complex random variables with EX11 = 0,E|X11| 2 = 1 and E|X11| 4 <∞, and let An = 1 N T 1/2 n XnX ∗ nT 1/2 n , where T 1/2 n is the square root of a nonnegative 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 pop...
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Let {a,}, i,j=1,2 ,..., be i.i.d. random variables, and for each n let M, = (l/s) V, Vz, where V, = (vi,). i = 1,2, . . . . n, j = 1,2, . . . . s = s(n), and n/s -+ y > 0 as n + co. Necessary and sufficient conditions are given to establish the convergence in distribution of certain random variables defined by M,. When E(uf,) < co these variables play an important role toward understanding the ...
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In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calcula...
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Let (vu) i, j = 1, 2 ,..., be i.i.d. standardized random variables. For each n, let V, = (v,,) i = 1, 2 ,..., n; j = 1, 2 ,..., s = s(n), where (n/s) -+ y > 0 as n + 03, and let M, = (l/s) V, Vi. Previous results [7,8] have shown the eigenvectors of M, to display behavior, for n large, similar to those of the corresponding Wishart matrix. A certain stochastic process X, on [0, 11, constructed f...
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あらまし パターン認識で用いられる,ベイズの定理から導かれる統計的識別関数は,パターンの確率分布が 正しく与えられたときに誤識別率が最小になる.パターンの確率分布は一般に未知であるため,正規分布を仮定 して,その平均ベクトルと共分散行列は学習サンプルからの推定値を用いることが多い.しかし,推定に用いる 学習サンプルが不足すると,推定値が誤差を含み,認識性能が低下することが知られている.平均ベクトルや共 分散行列の固有値の推定誤差についてはよく調査され,認識性能の低下を回避する方法が提案されている.しか し,共分散行列の固有ベクトルの推定誤差については,これまでほとんど考慮されてこなかった.本論文では, 学習サンプルが十分用意できない場合においても高精度な認識を行うことを目的とし,共分散行列の固有ベクト ルに誤差がある場合でも,2 次識別関数の主要部分であるマハラノビス距離を正しく推定...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2010
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-010-0298-3