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- Title
On Parametric Bootstrapping and Bayesian Prediction.
- Authors
Fushiki, Tadayoshi; Komaki, Fumiyasu; Aihara, Kazuyuki
- Abstract
We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback–Leibler divergence. Finally, we give some examples.
- Subjects
BAYESIAN analysis; PREDICTION theory; STATISTICAL decision making; DISTRIBUTION (Probability theory); STATISTICAL bootstrapping; ASYMPTOTIC theory in estimation theory
- Publication
Scandinavian Journal of Statistics, 2004, Vol 31, Issue 3, p403
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2004.02_127.x