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Delay Estimation for Some Stationary Diffusion‐type Processes

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  • Uwe Kuchler
  • Y. A. Kutoyants

Abstract

In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent and their limit distributions are described. The behaviour of the estimators is similar to the behaviour of corresponding estimators in change‐point problems. The question of asymptotical efficiency is also discussed.

Suggested Citation

  • Uwe Kuchler & Y. A. Kutoyants, 2000. "Delay Estimation for Some Stationary Diffusion‐type Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 405-414, September.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:405-414
    DOI: 10.1111/1467-9469.00197
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    Cited by:

    1. Pavel Gapeev & Uwe Küchler, 2008. "On large deviations in testing Ornstein–Uhlenbeck-type models," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 143-155, June.
    2. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
    3. Alexander Gushchin & Uwe Küchler, 2011. "On estimation of delay location," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 273-305, October.
    4. Gassem, Anis, 2009. "On parameter estimation for switching diffusion process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2484-2492, December.

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