English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper deals with the problem of parameter estimation based on certaineigenspaces of the empirical covariance matrix of an observed multidimensionaltime series, in the case where the time series dimension and the observationwindow grow to infinity at the same pace. In the area of large random matrixtheory, recent contributions studied the behavior of the extreme eigenvalues ofa random matrix and their associated eigenspaces when this matrix is subject toa fixed-rank perturbation. The present work is concerned with the situationwhere the parameters to be estimated determine the eigenspace structure of acertain fixed-rank perturbation of the empirical covariance matrix. Anestimation algorithm in the spirit of the well-known MUSIC algorithm forparameter estimation is developed. It relies on an approach recently developedby Benaych-Georges and Nadakuditi, relating the eigenspaces of extremeeigenvalues of the empirical covariance matrix with eigenspaces of theperturbation matrix. First and second order analyses of the new algorithm areperformed.

A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices