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.

翻译：我们考虑了对自动递减的Hilbertian 过程的自动关系操作员的估计问题。 通过Tikhonov 方法,我们确立了一个总体结果,得出估计的自动关系操作员的趋同率,这是根据估计的负差零和一个负差一个自动变异操作员的趋同率得出的,其结果一般是它能够容纳滞后的自动变差的任何一致估计,因此它可以适用于任何观察模式下的程序:完整、分散、稀少和/或测量错误。一个具有吸引力的特征是,其结果不需要对自动变差进行微妙的光谱衰减假设,而是取决于自然源条件。其结果通过对重要特殊案例的适用来说明。