Nonparametric Spline Regression with Autoregressive Moving Average Errors
研究了当误差服从自回归移动平均模型时，如何用样条非参数回归估计未知函数，并通过最大似然或交叉验证估计参数，利用状态空间形式实现高效算法。
We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given.