LAMN in a class of parametric models for null recurrent diffusions

Reinhard Höpfner () and Carina Zeller ()
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Reinhard Höpfner: Johannes Gutenberg Universität Mainz
Carina Zeller: Johannes Gutenberg Universität Mainz

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 9, 399-413

Abstract: Abstract We study statistical models for one-dimensional diffusions which are null recurrent. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A finite number of other parameters, of secondary importance, introduces additional flexibility for the modelization of the drift, and does not perturb the null recurrent behaviour. Under time-continuous observation we obtain local asymptotic mixed normality, state a local asymptotic minimax bound, and specify asymptotically optimal estimators.

Keywords: Diffusions; Null recurrence; Parametric inference; Information process; LAMN; Local asymptotic minimax bound; Asymptotically optimal estimators; 62 F 12; 62 M 05; 60 J 60 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11203-018-9175-y

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