均匀分布的线性近似贝叶斯估计

Linear Approximate Bayes Estimator for Uniform Distribution

本文利用线性贝叶斯方法估计均匀分布R(-θ,θ)的未知参数,提出了θ的线性近似贝叶斯估计(LABE),LABE具有封闭解析解的形式且便于使用.数值模拟表明本文提出的LABE与普通的贝叶斯估计(BE)很接近,其中BE由数值积分得到,我们也使用了所谓的强力算法来获得BE.进一步,我们比较了LABE与Lindley近似.在均方误差准则下,LABE相对于经典估计量的优越性也得到证明.

We employ a linear Bayes procedure to estimate the unknown parameter of the uniform distribution R(-θ,θ)and propose a linear approximate Bayes estimator(LABE)forθ,which has a closed analytic solution form and is convenient to use.Numerical simulations indicate that the proposed LABE is close to the ordinary Bayes estimator(BE),which is calculated by numerical integration and the so-called brute-force method as well.Furthermore,we compare the proposed LABE with the Lindley’s approximation.The superiorities of the LABE over the classical estimators are also established in terms of the mean squared error(MSE)criterion.