均方误（mean square error）

参数估计术语。参数\(\theta\)的估计量\(\hat{\theta}\)的离差平方的期望值，即\(MSE(\hat{\theta})=E(\hat{\theta}-\theta)^2\)。均方误有如下表达式：\(MSE(\hat{\theta})=E[(\hat{\theta}-E(\hat{\theta})]^2+[\theta-E(\hat{\theta})]^2=V(\hat{\theta})+[\theta-E(\hat{\theta})]^2\)，即估计量\(\hat{\theta}\)的均方误等于它的方差加上平方偏差（估计量的均值到 的误差的平方）。若\(\hat{\theta}\)是\(\theta\)的无偏估计，则\(\hat{\theta}\)的均方误等于它的方差。均方误是比较两个估计量的一个重要准则。若参数\(\theta\)有两个估计量\(\hat{\theta_1}\)与\(\hat{\theta_2}\)，它们的均方误是\(MSE(\hat{\theta_1})\)与\(MSE(\hat{\theta_2})\)，则\(\hat{\theta_1}\)与\(\hat{\theta_2}\)的相对效率定义为\(MSE(\hat{\theta_1})/MSE(\hat{\theta_2})\)。若相对效率小于1，则表明\(\hat{\theta_1}\)是比\(\hat{\theta_2}\)更有效的估计量。