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Local asymptotic quadraticity of stochastic process models based on stopping times

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  • Luschgy, Harald

Abstract

Consider a semimartingale whose drift and jump characteristic depend on an unknown parameter. The process is observed up to some stopping time [eta]. We establish conditions which ensure that the resulting statistical model admits locally a quadratic approximation of the log-likelihood process with asymptotics as [eta] --> [infinity]. This provides an important step in the solution of the inference problem for the unknown parameter based on random stopping.

Suggested Citation

  • Luschgy, Harald, 1995. "Local asymptotic quadraticity of stochastic process models based on stopping times," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 305-317, June.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:2:p:305-317
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    References listed on IDEAS

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    1. Höpfner, Reinhard, 1993. "Asymptotic inference for Markov step processes: Observation up to a random time," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 295-310, November.
    2. Greenwood, P. E. & Wefelmeyer, W., 1993. "Asymptotic minimax results for stochastic process families with critical points," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 107-116, January.
    3. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
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