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Asymptotic inference for Markov step processes: Observation up to a random time

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  • Höpfner, Reinhard

Abstract

Consider a Markov step process whose generator depends on an unknown one-dimensional parameter [theta]. Under a 'homogeneity' assumption concerning the family of information processes I[theta], [theta] [set membership, variant] [Theta], which does not require exact knowledge of the asymptotics of I[theta] under P[theta], there is an increasing sequence of bounded stopping times Un such that, observing X continuously over the random time interval [[0, Un]], the sequence of resulting statistical models is LAN as n --> [infinity], at every point [theta] [set membership, variant] [Theta], with local scale which does not depend on the parameter.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:2:p:295-310
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    Cited by:

    1. 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.

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