TY - JOUR
AU - Seal, Babulal
AU - Banerjee, Proloy
PY - 2024/09/29
Y2 - 2024/11/02
TI - Partial Bayes Estimation in a Normal Family
JF - Thailand Statistician
JA - Thail. Stat.
VL - 22
IS - 4
SE - Articles
DO -
UR - https://ph02.tci-thaijo.org/index.php/thaistat/article/view/256068
SP - 821-831
AB - <p><span class="fontstyle0">Areas of Bayesian analysis became vast throughout several decades. Bayes estimation, empirical<br>and hierarchical Bayes estimation are important areas among them. In multi-parameter case, notion<br>of ‘Partial Bayes (PB) Estimation’ is introduced and in <span class="CCword">N</span><span class="CCbrackets underline">(</span><span class="CCcommand">\theta</span> <span class="CCother">,</span> <span class="CCcommand">\sigma</span> <span class="CCoperator">^</span><span class="CCnumbers">2</span><span class="CCbrackets underline">)</span></span><span class="fontstyle0">, where parameters being unknown,<br>‘PB Estimation’ of </span><span class="fontstyle2">θ </span><span class="fontstyle0">is done by putting the estimator of </span><span class="fontstyle2">σ</span><span class="fontstyle4">2 </span><span class="fontstyle0">obtained by some other methods. When<br>we do not have enough information regarding the joint parameters of the model of the variable and<br>when we are estimating one parameter in presence of others, such method may be used instead of<br>empirical and hierarchical methods when the information about their parameters are not sufficient.<br>Integrated Risk of the PB estimator and Bayes estimator derived under squared error loss function are<br>compared along with the classical estimator MLE through simulation technique. From the results, it<br>is found that PB estimator has almost same risk values as that of the Bayes estimator, whereas the risk<br>of MLE is higher compared to both of the estimator. For illustrative purpose, a real dataset is used to<br>apply this PB estimation technique. PB is appropriate name to describe. However, partial Bayes term<br>has been used in different context of Bayesian hierarchical model and meta analysis.</span> </p>
ER -