Bayesian prediction regions and density estimation with type-2 censored data
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| Format: | Preprint |
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2024
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| _version_ | 1866913260866895872 |
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| author | Asgharzadeh, Akbar Marchand, Éric Nik, Ali Saadati |
| author_facet | Asgharzadeh, Akbar Marchand, Éric Nik, Ali Saadati |
| contents | For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first $m$ order statistics. We focus on the previously less explored aspects of predicting: (i) an arbitrary pair of future order statistics such as the next and last ones, as well as (ii) the next $N$ future order statistics. We provide explicit and exact Bayesian credible regions associated with Gamma priors, and constructed by identifying a region with a given credibility $1-λ$ under the Bayesian predictive density. For (ii), the HPD region is obtained, while a two-step algorithm is given for (i). The predictive distributions are represented as mixtures of bivariate Pareto distributions, as well as multivariate Pareto distributions. For the non-informative prior density choice, we demonstrate that a resulting Bayesian credible region has matching frequentist coverage probability, and that the resulting predictive density possesses the optimality properties of best invariance and minimaxity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian prediction regions and density estimation with type-2 censored data Asgharzadeh, Akbar Marchand, Éric Nik, Ali Saadati Statistics Theory 62F15, 62N01, 62N05, 62C10, 62C20 For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first $m$ order statistics. We focus on the previously less explored aspects of predicting: (i) an arbitrary pair of future order statistics such as the next and last ones, as well as (ii) the next $N$ future order statistics. We provide explicit and exact Bayesian credible regions associated with Gamma priors, and constructed by identifying a region with a given credibility $1-λ$ under the Bayesian predictive density. For (ii), the HPD region is obtained, while a two-step algorithm is given for (i). The predictive distributions are represented as mixtures of bivariate Pareto distributions, as well as multivariate Pareto distributions. For the non-informative prior density choice, we demonstrate that a resulting Bayesian credible region has matching frequentist coverage probability, and that the resulting predictive density possesses the optimality properties of best invariance and minimaxity. |
| title | Bayesian prediction regions and density estimation with type-2 censored data |
| topic | Statistics Theory 62F15, 62N01, 62N05, 62C10, 62C20 |
| url | https://arxiv.org/abs/2403.06718 |