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LAMN in a class of parametric models for null recurrent diffusions

Author

Listed:
  • Reinhard Höpfner

    (Johannes Gutenberg Universität Mainz)

  • Carina Zeller

    (Johannes Gutenberg Universität Mainz)

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.

Suggested Citation

  • Reinhard Höpfner & Carina Zeller, 2018. "LAMN in a class of parametric models for null recurrent diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 399-413, July.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9175-y
    DOI: 10.1007/s11203-018-9175-y
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    References listed on IDEAS

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    1. Khasminskii, R., 2001. "Limit distributions of some integral functionals for null-recurrent diffusions," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 1-9, March.
    2. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
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