PCA and eigen-inference for a spiked covariance model with largest eigenvalues of same asymptotic order

OPTIMAL SHRINKAGE OF EIGENVALUES IN THE SPIKED COVARIANCE MODEL By

Since the seminal work of Stein (1956) it has been understood that the empirical covariance matrix can be improved by shrinkage of the empirical eigenvalues. In this paper, we consider a proportional-growth asymptotic framework with n observations and pn variables having limit pn/n → γ ∈ (0, 1]. We assume the population covariance matrix Σ follows the popular spiked covariance model, in which s...

Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model

Abstract: This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow proportionally. The form of the joint limiting distribution is applied to conduct Johnson-Graybill-type tests, a family of approaches testing for signals i...

Largest eigenvalues and sample covariance matrices

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Asymptotics of the leading sample eigenvalues for a spiked covariance model

We consider a multivariate Gaussian observation model where the covariance matrix is diagonal and the diagonal entries are all equal to one except for a finite number which are bigger. We address the question of asymptotic behaviour of the eigenvalues of the sample covariance matrix when the sample size and the dimension of the observations both grow to infinity in such a way that their ratio c...