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. (C) 2022 The Author(s). Published by Elsevier B.V.

On the rate of convergence for the autocorrelation operator in functional autoregression / Caponera, Alessia; Panaretos, Vm. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 189:(2022), pp. 1-6. [10.1016/j.spl.2022.109575]

On the rate of convergence for the autocorrelation operator in functional autoregression

Caponera, A;
2022

Abstract

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. (C) 2022 The Author(s). Published by Elsevier B.V.
2022
Functional time series. Source condition. Tikhonov regularization
On the rate of convergence for the autocorrelation operator in functional autoregression / Caponera, Alessia; Panaretos, Vm. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 189:(2022), pp. 1-6. [10.1016/j.spl.2022.109575]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/236440
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