BAYESIANCOVARIANCEMATRIXESTIMATIONWITH NON-HOMOGENEOUS
Stéphanie Bidon, Olivier Besson · 2007
We address theproblem ofestimating thecovariance matrix Mp ofanobservation vector, usingK groups oftraining samples {Zk}IK,ofrespective sizeLk,whosecovariance matrices Mk maydiffer fromMp.A Bayesian modelis formulated whereweassume thatMp andthematrices Mk arerandom, withsomeprior distribution. Within this framework, wederive theminimummean-square error (MMSE)estimator ofMpwhichisimplemented using aGibbs-sampling strategy. Moreover, weconsider simpler estimators based on aweighted sumofthesample covariance matrices ofZk. We derive anexpression fortheweights that result inminimummeansquare error (MSE), within this class ofestimators. Numerical simulations arepresented toillustrate theperformances ofthedifferent estimation schemes.