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A shrinkage predictive distribution for multivariate normal observables. (English) Zbl 0985.62024

Summary: We investigate shrinkage methods for constructing predictive distributions. We consider the multivariate normal model with a known covariance matrix and show that there exists a shrinkage predictive distribution dominating the Bayesian predictive distribution based on the vague prior when the dimension is not less than three. Kullback-Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function.

MSC:

62F15 Bayesian inference
62J07 Ridge regression; shrinkage estimators (Lasso)
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