Optimal high-dimensional shrinkage covariance estimation for elliptical distributions

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

4 Citations (Scopus)

Abstract

We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle) shrinkage parameters that obtain the minimum mean-squared error (MMSE) between the shrinkage SCM and the true covariance matrix when sampling from an elliptical distribution. Subsequently, we show how the oracle shrinkage parameters can be consistently estimated under the random matrix theory regime. Simulations show the advantage of the proposed estimator over the conventional shrinkage SCM estimator due to Ledoit and Wolf (2004). The proposed shrinkage SCM estimator often provides significantly better performance than the Ledoit-Wolf estimator and has the advantage that consistency is guaranteed over the whole class of elliptical distributions with finite 4th order moments.
Original languageEnglish
Title of host publication2017 25th European Signal Processing Conference (EUSIPCO)
PublisherIEEE
Pages1639 - 1643
Number of pages5
ISBN (Electronic)978-0-9928626-7-1
ISBN (Print)978-1-5386-0751-0
DOIs
Publication statusPublished - Oct 2017
MoE publication typeA4 Article in a conference publication
EventEuropean Signal Processing Conference - Kos Island, Greece, Kos, Greece
Duration: 28 Aug 20172 Sep 2017
Conference number: 25
https://www.eusipco2017.org
https://www.eusipco2017.org/

Publication series

NameEuropean Signal Processing Conference
ISSN (Electronic)2076-1465

Conference

ConferenceEuropean Signal Processing Conference
Abbreviated titleEUSIPCO
Country/TerritoryGreece
CityKos
Period28/08/201702/09/2017
Internet address

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