带有缺数据下Laplace分布的参数估计

Parameter Estimation of Laplace Distribution with Missing Data

研究了在样本数据缺失的情况下对Laplace分布参数的极大似然估计,并在共轭先验分布为逆伽马分布下和不同损失函数情况下计算出了参数的Bayes和E-Bayes估计的表达式。最后通过随机模拟,得到了对各种估计的均值和均方误差。且结果表明,Bayes和E-Bayes的均方误差比极大似然估计的均方误差要小。

The maximum likelihood estimation of the parameters of the Laplace distribution in the face of missing sample data is investigated,and expressions for the Bayes and E-Bayes estimates of the parameters are obtained under the conjugate prior distribution as the inverse gamma distribution and with different loss functions.At last,the mean and mean square error of the various kinds of estimates are derived by random simulation.And the results show that the mean summed errors of Bayes and E-Bayes are smaller than the mean square error of the great likelihood estimation.