论文标题
关于功能自动化中自相关运算符的收敛速率
On the rate of convergence for the autocorrelation operator in functional autoregression
论文作者
论文摘要
我们考虑估计自回归希尔伯特式过程的自相关操作员的问题。通过Tikhonov方法，我们建立了一个总体结果，该结果可以产生估计的自相关算子的收敛速率，这是估计滞后零零和滞后一个自动助行操作员的收敛速率的函数。结果通常是因为它可以容纳对滞后自动载体的任何一致估计器。因此，它可以在任何观察方式下应用于过程：完整，离散，稀疏和/或使用测量误差。一个吸引人的特征是，结果不需要在自动载体上进行微妙的光谱衰减假设，而是基于自然源条件。结果通过在重要特殊情况下的应用来说明。
We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yields the convergence rate of the estimated autocorrelation operator as a function of the rate of convergence of the estimated lag zero and lag one autocovariance operators. The result is general in that it can accommodate any consistent estimators of the lagged autocovariances. Consequently it can be applied to processes under any mode of observation: complete, discrete, sparse, and/or with measurement errors. An appealing feature is that the result does not require delicate spectral decay assumptions on the autocovariances but instead rests on natural source conditions. The result is illustrated by application to important special cases.
