均匀分布的线性近似贝叶斯估计
Linear Approximate Bayes Estimator for Uniform Distribution
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摘要: 本文利用线性贝叶斯方法估计均匀分布R(-\theta,\theta)的未知参数,提出了\theta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.Abstract: We employ a linear Bayes procedure to estimate the unknown parameter of the uniform distribution R(-\theta,\theta) and propose a linear approximate Bayes estimator (LABE) for \theta, 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.