On the uniqueness of the M. L. estimates in curved exponential families

Andrej Pázman

Kybernetika (1986)

  • Volume: 22, Issue: 2, page 124-132
  • ISSN: 0023-5954

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Pázman, Andrej. "On the uniqueness of the M. L. estimates in curved exponential families." Kybernetika 22.2 (1986): 124-132. <http://eudml.org/doc/28179>.

@article{Pázman1986,
author = {Pázman, Andrej},
journal = {Kybernetika},
keywords = {Curved families; exponential families; full rank differentiable sufficient statistics; maximum likelihood estimate; Gaussian nonlinear regression; beta-distribution; Generalized curved exponential families},
language = {eng},
number = {2},
pages = {124-132},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the uniqueness of the M. L. estimates in curved exponential families},
url = {http://eudml.org/doc/28179},
volume = {22},
year = {1986},
}

TY - JOUR
AU - Pázman, Andrej
TI - On the uniqueness of the M. L. estimates in curved exponential families
JO - Kybernetika
PY - 1986
PB - Institute of Information Theory and Automation AS CR
VL - 22
IS - 2
SP - 124
EP - 132
LA - eng
KW - Curved families; exponential families; full rank differentiable sufficient statistics; maximum likelihood estimate; Gaussian nonlinear regression; beta-distribution; Generalized curved exponential families
UR - http://eudml.org/doc/28179
ER -

References

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  1. S. Amari, Differential geometry of curved exponential families - curvatures and information loss, Ann. Statist. 10 (1982), 357-387. (1982) Zbl0507.62026MR0653513
  2. O. Barndorff-Nielsen, Information and Exponential Families in Statistical Theory, Wiley, Chichester 1979. (1979) MR0489333
  3. B. Efron, The geometry of exponential families, Ann. Statist. 6 (1978), 362-376. (1978) Zbl0436.62027MR0471152
  4. V. Jarník, Diferenciální počet II, (Differential Calculus). NČSAV, Praha 1956. (1956) 
  5. A. Pázman, Nonlinear least squares - uniqueness versus ambiguity, Math. Operationsforsch. Statist. Ser. Statist. 15 (1984), 323-336. (1984) MR0756337
  6. A. Pázman, Probability distribution of the multivariate nonlinear least squares estimates, Kybernetika 20 (1984), 209-230. (1984) MR0763647
  7. S. Sternberg, Lectures on Differential Geometry, Second printing. Prentice-Hall, Englewood Cliffs 1965. (1965) MR0193578

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