On Efficiency and Exponential Families in Stochastic Process Estimation

Heyde, C. C.; Feigin, P. D.

doi:10.1007/978-94-010-1842-5_18

On Efficiency and Exponential Families in Stochastic Process Estimation

C. C. Heyde⁴ &
P. D. Feigin⁴

Conference paper

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9 Citations

Part of the book series: NATO Advanced Study Institutes 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.

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References

Anderson, T. W. (1959). Ann. Math. Statist. 30, 676–687.
Article MathSciNet MATH Google Scholar
Billingsley, P. (1961). Statistical Inference for Markov Processes. University of Chicago Press, Chicago.
MATH Google Scholar
Hall, P. G. and Heyde, C. C. (1974). Manuscript under preparation.
Google Scholar
Harris, T. E. (1948). Ann. Math. Statist. 19, 474–494.
Article MATH Google Scholar
Heyde, C. C. (1974). Remarks on efficiency in estimation for branching processes. To appear in Biometrika.
Google Scholar
Johnson, N. L. and Kotz, S. (1969). Discrete Distributions. Houghton Mifflin, Boston.
MATH Google Scholar
Neveu, J. (1970). Calcul des Probabilites. 2nd ed. Masson et Cie, Paris.
MATH Google Scholar
Ord, J. K. (1972). Families of Frequency Distributions. Griffin, London.
MATH Google Scholar
Rao, C. R. (1965). Linear Statistical Inference and Its Applications. Wiley, New York.
MATH Google Scholar
Roussas, G. G. (1972). Contiguity of Probability Measures. Cambridge University Press, Cambridge.
Book MATH Google Scholar

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Authors and Affiliations

Department of Statistics, Australian National University, Canberra, Australia
C. C. Heyde & P. D. Feigin

Authors

C. C. Heyde
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P. D. Feigin
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Editor information

Editors and Affiliations

The Pennsylvania State University, University Park, Pa., USA
G. P. Patil
Temple University, Philadelphia, Pa., USA
S. Kotz
University of Warwick, Coventry, England
J. K. Ord

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Heyde, C.C., Feigin, P.D. (1975). On Efficiency and Exponential Families in Stochastic Process Estimation. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1842-5_18

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DOI: https://doi.org/10.1007/978-94-010-1842-5_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1844-9
Online ISBN: 978-94-010-1842-5
eBook Packages: Springer Book Archive

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