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New results on strong-consistency, in the Hilbert-Schmidt and trace operatornorms, are obtained, in the parameter estimation of an autoregressiveHilbertian process of order one (ARH(1) process). In particular, astrongly-consistent diagonal componentwise estimator of the autocorrelationoperator is derived, based on its empirical singular value decomposition.

A note on strong-consistency of componentwise ARH(1) predictors