The vector LMMSE Estimator

The vector LMMSEEstimatorGajitzki PaulMaster 1 IRT

The LMMSE Estimator• The scalar solution can be applied, and weobtain• The minimum bayesian MSE is:

The LMMSE Estimator• The scalar LMMSE estimator can be combinedinto a vector estimator

The LMMSE Estimator• By a similar aproach we can find the BayesianMSE matrix• The minimum Bayesian is

The LMMSE Estimator• LMMSE estimator comutes over liniartransformations• The LMMSE estimator of a sum of unkownparameters is the sum of the individualestimators

The LMMSE Estimator• TH. GAUSS-MARKOV:if data arederscribed by the Bayesian model form• Then the LMMSE estimator is:

The LMMSE Estimator• The performance of the estimator is measuredby the error :• Whose covariance matrix is :

The LMMSE Estimator• CONCLUSION:Although suboptimal, the LMMSE estimator isin practice very useful,being available in closedform and depending only by the means and thecovariances

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