The Experts below are selected from a list of 1054791 Experts worldwide ranked by ideXlab platform

Lansun Chen - One of the best experts on this subject based on the ideXlab platform.

Jianjun Jiao - One of the best experts on this subject based on the ideXlab platform.

Jian-feng Yao - One of the best experts on this subject based on the ideXlab platform.

  • on sample eigenvalues in a generalized spiked Population Model
    Journal of Multivariate Analysis, 2012
    Co-Authors: Zhidong Bai, Jian-feng Yao
    Abstract:

    In the spiked Population Model introduced by Johnstone (2001) [11], the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein (2006) [5] establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. In a recent work Bai and Yao (2008) [4], we have provided the limiting distributions for these extreme sample eigenvalues. In this paper, we extend this theory to a generalized spiked Population Model where the base Population covariance matrix is arbitrary, instead of the identity matrix as in Johnstone's case. As the limiting spectral distribution is arbitrary here, new mathematical tools, different from those in Baik and Silverstein (2006) [5], are introduced for establishing the almost sure convergence of the sample eigenvalues generated by the spikes.

  • On determining the number of spikes in a high-dimensional spiked Population Model
    Random Matrices. Theory and Applications, 2012
    Co-Authors: Damien Passemier, Jian-feng Yao
    Abstract:

    In a spiked Population Model, the Population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture Model) or economics (factor Model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

  • Limit theorems for sample eigenvalues in a generalized spiked Population Model
    2008
    Co-Authors: Zhidong Bai, Jian-feng Yao
    Abstract:

    In the spiked Population Model introduced by Johnstone (2001),the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein (2006) establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. In a recent work (Bai and Yao, 2008), we have provided the limiting distributions for these extreme sample eigenvalues. In this paper, we extend this theory to a {\em generalized} spiked Population Model where the base Population covariance matrix is arbitrary, instead of the identity matrix as in Johnstone's case. New mathematical tools are introduced for establishing the almost sure convergence of the sample eigenvalues generated by the spikes.

  • Central limit theorems for eigenvalues in a spiked Population Model
    Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2008
    Co-Authors: Zhidong Bai, Jian-feng Yao
    Abstract:

    In a spiked Population Model, the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). This Model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. This paper establishes the limiting distributions of these extreme sample eigenvalues. As another important result of the paper, we provide a central limit theorem on random sesquilinear forms.

Wen Long - One of the best experts on this subject based on the ideXlab platform.

W. Robertson - One of the best experts on this subject based on the ideXlab platform.