Bayesian Inference and Prediction for Normal Distribution Based on Records

Akbar Asgharzadeh (), Reza Valiollahi (), Adeleh Fallah () and Saralees Nadarajah ()
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Akbar Asgharzadeh: University of Mazandaran - Iran
Reza Valiollahi: Semnan University - Iran
Adeleh Fallah: Payame Noor University - Iran
Saralees Nadarajah: University of Manchester - UK

Statistica, 2018, vol. 78, issue 1, 15-36

Abstract: Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.

Keywords: Bayesian prediction; Best linear unbiased estimators; Maximum likelihood estimators; Record data (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bot:rivsta:v:78:y:2018:i:1:p:15-36

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