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On Efficiency and Exponential Families in Stochastic Process Estimation

  • C. C. Heyde
  • P. D. Feigin
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)

Summary

A general definition of efficiency for stochastic process estimation is proposed and some of its ramifications are explored. Of particular importance in the definition is the form of the derivative of the logarithm of the likelihood. The question of the simplest possible form for this leads on to a discussion of extensions of the concepts of sufficiency and exponential families, the latter in a Markov process context. The paper concludes with several illustrative examples.

Key Words

Stochastic process estimation efficiency sufficiency exponential family maximum likelihood Martingale limit theory branching process first order autoregression power series distributions 

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References

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Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • C. C. Heyde
    • 1
  • P. D. Feigin
    • 1
  1. 1.Department of StatisticsAustralian National UniversityCanberraAustralia

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