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Shrinkage

The classical-equivalent estimator is also known as Bayes-Stein shrinkageestimator.

• Classical-equivalent shrinkage

θ̂classical

low confidence←− θcl_eqposterior

high confidence−→ θpriprior

(23.13)

• Estimation uncertainty shrinkage

s2θhigh confidence−→ 0 (23.14)

The MAP classical equivalent (23.9) is a maximum likelihood estimator(22.5), with a shrinkage penalty function

θ̂MAP ≡ argmaxθ{ln fθ(x) + φ(θ)} (23.15)

where the penalty is given by the prior φ(θ) ≡ ln fpri(θ).

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Feb-24-2017 - Last update