Abstract
Let Y and Z be two random vectors with joint density f(y, z|θ), where θ∈Θ is an unknown parameter vector, and consider predicting Z based on y, the observed value of Y. We investigate Bayesian and decision-theoretic approaches to this problem, taking into account the loss function and the prior distribution of θ. Exploring connections between statistical prediction and decision theory, we find that a prediction problem can be reduced to a standard decision theory problem if the induced loss function is allowed to depend on the observed data y in addition to the unknown parameter θ and the decision d. In general, the predictive posterior density f(z|y) may not contain all information necessary for obtaining optimum predictions, but the posterior density f(θ|y) is adequate for that purpose. Some admissibility results are also discussed.
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Nayak, T.K., El-Baz, A. (2006). On Bayesian and Decision-Theoretic Approaches to Statistical Prediction. In: Balakrishnan, N., Sarabia, J.M., Castillo, E. (eds) Advances in Distribution Theory, Order Statistics, and Inference. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4487-3_26
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DOI: https://doi.org/10.1007/0-8176-4487-3_26
Publisher Name: Birkhäuser Boston
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