Efficient Generalized Cross-Validation for State Space Models
针对状态空间表示的信号加噪声模型，提出一种高效计算影响矩阵迹的方法，仅需在普通卡尔曼滤波中增加一个方程即可实现O(n)的广义交叉验证，适用于回归中的样条平滑和季节时间序列的方差分量模型。
For a signal plus noise model with a state space representation, an efficient procedure is given for obtaining the trace of the influence matrix, where the influence matrix expresses the estimated signal vector as a linear combination of the observed data. This allows an O(n) evaluation of the generalized cross-validation criterion function. Our approach is very efficient, requiring the addition of only one equation to the ordinary Kalman filter, and extends to models with linear regressors in the observation equation. Important applications are to spline smoothing in regression and to variance components models for seasonal time series.