An admissible estimator of a lower-bounded scale parameter under squared-log error loss function

Eisa Mahmoudi; Hojatollah Zakerzadeh

Kybernetika (2011)

  • Volume: 47, Issue: 4, page 595-611
  • ISSN: 0023-5954

Abstract

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Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.

How to cite

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Mahmoudi, Eisa, and Zakerzadeh, Hojatollah. "An admissible estimator of a lower-bounded scale parameter under squared-log error loss function." Kybernetika 47.4 (2011): 595-611. <http://eudml.org/doc/196491>.

@article{Mahmoudi2011,
abstract = {Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.},
author = {Mahmoudi, Eisa, Zakerzadeh, Hojatollah},
journal = {Kybernetika},
keywords = {admissibility; Bayes estimator; truncated parameter spaces; squared-log error loss; Bayes estimator; truncated parameter spaces},
language = {eng},
number = {4},
pages = {595-611},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An admissible estimator of a lower-bounded scale parameter under squared-log error loss function},
url = {http://eudml.org/doc/196491},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Mahmoudi, Eisa
AU - Zakerzadeh, Hojatollah
TI - An admissible estimator of a lower-bounded scale parameter under squared-log error loss function
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 4
SP - 595
EP - 611
AB - Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.
LA - eng
KW - admissibility; Bayes estimator; truncated parameter spaces; squared-log error loss; Bayes estimator; truncated parameter spaces
UR - http://eudml.org/doc/196491
ER -

References

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  1. Berry, J. C., Minimax estimation of a restricted exponential location parameter, Statist. Decision 11 (1993), 307–316. (1993) Zbl0792.62006MR1261841
  2. Blyth, C. R., 10.1214/aoms/1177729690, Ann. Math. Statist. 22 (1951), 22–42. (1951) MR0039966DOI10.1214/aoms/1177729690
  3. Brown, L., 10.1214/aoms/1177698503, Ann. Math. Statist. 29(1) (1968), 29–48. (1968) MR0222992DOI10.1214/aoms/1177698503
  4. Ferguson, T. S., Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York 1967. (1967) Zbl0153.47602MR0215390
  5. Hoaglin, D. C., 10.1080/01621459.1975.10480317, J. Amer. Statist. Assoc. 70 (1975), 880–888. (1975) Zbl0327.62029DOI10.1080/01621459.1975.10480317
  6. Jozani, M. Jafari, Nematollahi, N., Shafie, K., An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss, Statist. Prob. Letter 60 (2002), 434–444. (2002) MR1947183
  7. Katz, W., 10.1214/aoms/1177705146, Ann. Math. Statist. 32 (1961), 136–142. (1961) MR0119287DOI10.1214/aoms/1177705146
  8. Lehmann, E. L., Casella, G., Theory of Point Estimation, Second edition. Springer-Verlag, John Wiley, New York 1998. (1998) Zbl0916.62017MR1639875
  9. Moors, J. J. A., Estimation in Truncated Parameter Spaces, Ph.D Thesis, Tilburg University Tilburg, The Netherlands 1985. (1985) 
  10. Moors, J. J. A., Houwelingen, J. C. van, 10.1111/j.1467-9574.1993.tb01416.x, Statist. Neerlandica 47 (1993), 185–198. (1993) MR1243854DOI10.1111/j.1467-9574.1993.tb01416.x
  11. Parsian, A., Nematollahi, N., 10.1016/0378-3758(95)00026-7, J. Statis. Plann. Infer. 52 (1996), 77–91. (1996) Zbl0846.62021MR1391685DOI10.1016/0378-3758(95)00026-7
  12. Pitman, E. J. J., The estimation of location and scale parameters of a continuous population of any given form, Biometrika 30 (1938), 391–421. (1938) 
  13. Pitman, E. J. J., Some Basic Theory for Statistical Inference, Chapman Hall, London 1979. (1979) Zbl0442.62002MR0549771
  14. Rahman, M. S., Gupta, R. P., Family of transformed chi-square distributions, Comm. Statist. Theory Methods 22 (1993), 135–146. (1993) MR1209502
  15. Robertson, T., Wright, F. T., Dijkstra, R. L., Order Restricted Statistical Inference, John Wiley, New York 1988. (1988) MR0961262
  16. Farsipour, N. Sanjari, Zakerzadeh, H., Estimation of a gamma scale parameter under asymmetric squared-log error loss, Comm. Statist. Theory Methods 34 (2005), 1–9. (2005) MR2189422
  17. Shao, P., Strawderman, W. E., 10.2307/3315693, Canad. J. Statist. 24 (1996), 105–114. (1996) Zbl0846.62006MR1394744DOI10.2307/3315693
  18. Stein, C., 10.1214/aoms/1177706080, Ann. Math. Statist. 30 (1959), 970–979. (1959) MR0109392DOI10.1214/aoms/1177706080
  19. Eeden, C. van, 10.2307/3315365, Canada. J. Statist. 23 (1995), 245–256. (1995) MR1363590DOI10.2307/3315365
  20. Eeden, C. van, 10.1016/S0167-7152(99)00114-5, Statist. Prob. Lett. 46 (2000), 283–286. (2000) DOI10.1016/S0167-7152(99)00114-5
  21. Eeden, C. van, Zidek, J. V., Group-Bayes estimation of the exponential mean: A retrospective view of the wald theory, In: Statistical Decision Theory and Related Topics, V (S. S. Gupta and J. Berger, eds.), Springer, Berlin 1994, pp. 35–49. (1994) MR1286293
  22. Eeden, C. van, Zidek, J. V., 10.1007/BF02562677, Test 3 (1994), 125–143. (1994) MR1293111DOI10.1007/BF02562677
  23. Eeden, C. van, Zidek, J. V., 10.1007/BF02562705, Test 3 (1994), 247. (1994) MR1293111DOI10.1007/BF02562705

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