基于EM算法的光滑参数选择

在非参数建模中,可以通过最小化均方误差（mean squared error）来优化光滑参数λ,即需要刻画出均方误差随λ的变化趋势,进而使均方误差最小的λ值即为最优的估计值,但在实际应用中并不知道回归函数的显示表达式,因此方法具有一定的局限性;通过样条回归模型与混合效应模型之间的关系,结合极大似然理论与EM算法去优化光滑参数λ.

Smoothing Parameter Selection Based on EM Algorithm

In nonparametric modeling, smoothing parameter h is optimized by minimized mean square error, i. e., the changing trend of mean square error needs to be described with the change of h, furthermore, the minimum 5, value of mean square error is made to be the optimal estimated value, however, in practical application, the implicit expression of regression function is not known, as a result, this method has certain limitation. Smoothing parameter h is optimized by the relation between spline regression model and mixed effect model and by combination of maximum likelihood theory and EM algorithm.