Nonparametric bootstrap prediction

Fushiki, Tadayoshi; Komaki, Fumiyasu; Aihara, Kazuyuki

doi:10.3150/bj/1116340296

Cited by 19 publications

(16 citation statements)

References 11 publications

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“…The proof of this fact is similar to Theorem 4 in Fushiki et al (2003). When p and q are the same, this prior coincides with the maximum likelihood prior.…”

supporting

confidence: 60%

On Parametric Bootstrapping and Bayesian Prediction

Fushiki

Komaki

Aihara

2004

Scandinavian J Statistics

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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. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

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“…The proof of this fact is similar to Theorem 4 in Fushiki et al (2003). When p and q are the same, this prior coincides with the maximum likelihood prior.…”

supporting

confidence: 60%

On Parametric Bootstrapping and Bayesian Prediction

Fushiki

Komaki

Aihara

2004

Scandinavian J Statistics

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“…Finally, the asymptotic expansion ofp BB (x N+1 ; x N ) is obtained by the Taylor expansion. The asymptotic expansion ofp B (x N+1 ; x N ) is shown in Fushiki et al (2005). By comparing these results, we obtain…”

Section: Asymptotic Analysismentioning

confidence: 94%

Bayesian bootstrap prediction

Fushiki¹

2010

Journal of Statistical Planning and Inference

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“…The predictive distribution in equation was named the “parametric bootstrap predictive distribution” by Harris [] and has been further developed by other authors [e.g., Basu and Harris , ; Vidoni , ; Fushiki et al ., ; Fushiki , ]. A similar approach termed “bagging predictors” [e.g., Breiman , ] is used in the field of machine learning.…”

Section: A Data‐based Comparison Frameworkmentioning

confidence: 99%

Data‐based comparison of frequency analysis methods: A general framework

Renard¹,

Kochanek

Lang³

et al. 2013

Water Resources Research

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[1] An abundance of methods have been developed over the years to perform the frequency analysis (FA) of extreme environmental variables. Although numerous comparisons between these methods have been implemented, no general comparison framework has been agreed upon so far. The objective of this paper is to build the foundation of a data-based comparison framework, which aims at complementing more standard comparison schemes based on Monte Carlo simulations or statistical testing. This framework is based on the following general principles: (i) emphasis is put on the predictive ability of competing FA implementations, rather than their sole descriptive ability measured by some goodness-of-fit criterion; (ii) predictive ability is quantified by means of reliability indices, describing the consistency between validation data (not used for calibration) and FA predictions; (iii) stability is also quantified, i.e., the ability of a FA implementation to yield similar estimates when calibration data change; and (iv) the necessity to subject uncertainty estimates to the same scrutiny as point estimates is recognized, and a practical approach based on the use of the predictive distribution is proposed for this purpose. This framework is then applied to a case study involving 364 gauging stations in France, where 10 FA implementations are compared. These implementations correspond to the local, regional, and local-regional estimation of Gumbel and generalized extreme value distributions. Results show that reliability and stability indices are able to reveal marked differences between FA implementations. Moreover, the case study also confirms that using the predictive distribution to indirectly scrutinize uncertainty estimates is a viable approach, with distinct FA implementations showing marked differences in the reliability of their uncertainty estimates. The proposed comparison framework therefore constitutes a valuable tool to compare the predictive reliability of competing FA implementations, along with the reliability of their uncertainty estimates.

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Nonparametric bootstrap prediction

Cited by 19 publications

References 11 publications

On Parametric Bootstrapping and Bayesian Prediction

On Parametric Bootstrapping and Bayesian Prediction

Bayesian bootstrap prediction

Data‐based comparison of frequency analysis methods: A general framework

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