On local asymptotic normality for functional autoregressive processes

Nesrine Kara-Terki and Tahar Mourid

Journal of Multivariate Analysis, 2016, vol. 148, issue C, 120-140

Abstract: We establish Local Asymptotic Normality (LAN) and Uniform Local Asymptotic Normality (ULAN) conditions for a class of function space valued autoregressive processes when the correlation operator depends on an unknown one-dimensional parameter. We then derive Hajek minimax bound, consistency, asymptotic normality and efficiency of the conditional maximum likelihood estimator yielding their optimality. A simulation studies illustrate the performance of the estimators.

Keywords: Functional autoregressive processes; Local asymptotic normality; Hajek bound; Maximum likelihood estimator; Efficiency (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2016.02.017

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