On predictive density estimation for Gamma models with parametric constraints

LMoudden, Aziz; Marchand, Éric; Kortbi, Othmane; Strawderman, William E.

doi:10.1016/j.jspi.2017.01.003

Cited by 11 publications

(2 citation statements)

References 24 publications

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“…Minimax Bayes predictive densities for unconstrained parameter spaces are studied in [35,4]. Minimax predictive densities under parametric constraints are studied in [16,32,36]. Shrinkage priors for Bayes predictive densities under Gaussian models are investigated in [28,17,26,39]; see also [25,5] for the cases where the variances are unknown.…”

Section: Literature Reviewmentioning

confidence: 99%

Minimax Predictive Density for Sparse Count Data

Yano

Kaneko

Komaki

2018

Preprint

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This paper discusses predictive densities under the Kullback-Leibler loss in high-dimensional sparse count data models. In particular, Poisson sequence models under sparsity constraints are discussed. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive densities that attain exact asymptotic minimaxity in sparse Poisson sequence models. We also show that our class with an estimator of unknown sparsity level plugged-in is adaptive in the exact minimax sense. For application, we extend our results to settings with quasi-sparsity and with missing-completely-at-random observations. The simulation studies as well as applications to real data demonstrate the efficiency of the proposed Bayes predictive densities.

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Section: Literature Reviewmentioning

confidence: 99%

Minimax Predictive Density for Sparse Count Data

Yano

Kaneko

Komaki

2018

Preprint

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“…Proof. (I) It follows from Lemma 2.1 that 15) with G(θ, c) = E e − |θ + (X)−θ| 2 2γ 0 (c) and the given notation. Calculations yield the expression G(θ, c) =…”

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confidence: 99%

On Predictive Density Estimation under α-Divergence Loss

LMoudden

Marchand

2019

Math. Meth. Stat.

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Based on X ∼ N d (θ, σ 2 X I d ), we study the efficiency of predictive densities under α−divergence loss L α for estimating the density ofWe identify a large number of cases where improvement on a plug-in density are obtainable by expanding the variance, thus extending earlier findings applicable to Kullback-Leibler loss. The results and proofs are unified with respect to the dimension d, the variances σ 2 X and σ 2 Y , the choice of loss L α ; α ∈ (−1, 1). The findings also apply to a large number of plug-in densities, as well as for restricted parameter spaces with θ ∈ Θ ⊂ R d . The theoretical findings are accompanied by various observations, illustrations, and implications dealing for instance with robustness with respect to the model variances and simultaneous dominance with respect to the loss.

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Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location

Hamura

Kubokawa

2021

Metrika

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On predictive density estimation for Gamma models with parametric constraints

Cited by 11 publications

References 24 publications

Minimax Predictive Density for Sparse Count Data

Minimax Predictive Density for Sparse Count Data

On Predictive Density Estimation under α-Divergence Loss

Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location

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