کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1145514 1489661 2015 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions
چکیده انگلیسی

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. The optimal nonlinear shrinkage formula depends on unknown population quantities and is thus not available. It is, however, possible to consistently estimate an oracle nonlinear shrinkage, which is motivated on asymptotic grounds. A key tool to this end is consistent estimation of the set of eigenvalues of the population covariance matrix (also known as the spectrum), an interesting and challenging problem in its own right. Extensive Monte Carlo simulations demonstrate that our methods have desirable finite-sample properties and outperform previous proposals.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 139, July 2015, Pages 360–384
نویسندگان
, ,