KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 2

Comparing Bhattacharyya and Kshirsagar bounds with bootstrap method

M. Khorashadizadeh0000-0001-7732-1599
S. Nayeban0000-0002-2527-9007
A.h. Rezaei Roknabadi0000-0002-3420-9027
G.r. Mohtashami Borzadaran0000-0002-8841-1386
Sayfa
—
Yayın Tarihi
2019-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Many studies have been done on the lower bounds for the variance of an unbiased estimator of the parameter.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the class of unbiased estimators for the parameter functions, the variance of estimator is one of the basic criteria to compare and evaluate the accuracy of the estimators.
📊
Temel Bulgular & Veri:In many cases the variance has complicated form and we can not compute it, so, by lower bounds, we can approximate it.
💡
Sonuç & Katkı:Many studies have been done on the lower bounds for the variance of an unbiased estimator of the parameter.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bhattacharyya bound · Bootstrap method · Cramer-Rao bound

Abstract

In the class of unbiased estimators for the parameter functions, the variance of estimator is one of the basic criteria to compare and evaluate the accuracy of the estimators. In many cases the variance has complicated form and we can not compute it, so, by lower bounds, we can approximate it. Many studies have been done on the lower bounds for the variance of an unbiased estimator of the parameter.

🔖

Bu Makaleye Atıf Yap

Khorashadizadeh, M., Nayeban, S., Roknabadi, A. R., Borzadaran, G. M. (2019). Comparing Bhattacharyya and Kshirsagar bounds with bootstrap method. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://ajindex.com/articles/1402823

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (36)

  1. Alharbi, A. A. G. On the convergence of the Bhattacharyya bounds in the multiparametric case, Applicationes Mathematicae, 22, (3), 339-349, 1994.
  2. Asrabadi, B. R. Estimation in the Pareto distribution, Metrika, 37, 199-205, 1990.
  3. Bartoszewicz, J. On the convergence of Bhattacharyya bounds in the multiparameter case, Zastos. Mat., 16, 601-608, 1980.
  4. Basu, A. P. Estimates of reliability for some distributions useful in life testing, Technometrics, 6, 215-219, 1964.
  5. Bhattacharyya, A. On some analogues of the amount of information and their use in statistical estimation, Sankhya A, 8, 1-14, 1946.
  6. Bhattacharyya, A. On some analogues of the amount of information and their use in statistical estimation II, Sankhya A, 8, 201-218, 1947.
  7. Blight, B. J. N. and Rao, R. V. The convergence of Bhattacharyya bounds, Biometrika, 61, (1), 137-142, 1974.
  8. Chapman, D. G. and Robbins, H. Minimum variance estimation without regularity assumptions. Ann. Math. Statist., 22, 581-586, 1951.
  9. Cramer, H. Mathematical Methods of Statistics, University Press, Princeton, 1946.
  10. Efron, B. Bootstrap methods: Another look at the jackknife, The Annals of Statistics, 7, 1. 1-26, 1979.
  11. Ghosh, J. K. and Sathe, S. Convergence of Bhattacharyya bounds-Revisited, Sankhya, The Indian Journal of Statistics, 49, Series A, 37-42, 1987.
  12. Haldan, J. B. S. On the method of estimating frequencies, Ann. Eugen., 11, 182-187, 1945.
  13. Hammersley, J. M. On estimating restricted parameters, J. Roy. Statist. Soc. Ser. B, 12, 192-240, 1950.
  14. Khorashadizadeh, M. and Mohtashami Borzadaran, G. R. The structure of Bhattacharyya matrix in natural exponential family and its role in approximating the variance of a statistics, J. Statistical Research of Iran (JSRI), 4, (1), 29-46, 2007.
  15. Kotz, S., Lumelski, I. P., and Pensky, M. The stress-strength Model and its Generalizations: Theory and Applications, World Scientific, 2003.
  16. Kshirsagar, A. M. An extension of the Chapman-Robbins inequality, J. Indian Statist. Assoc., 38, 355-362, 2000.
  17. Miller, K. S. On the inverse of the sum of matrices, Mathematics Magazine, 54, 2, 67-72, 1981.
  18. Mohtashami Borzadaran, G. R. Results related to the Bhattacharyya matrices, Sankhya A, 63, 1, 113-117, 2001.
  19. Mohtashami Borzadaran, G. R. A note via diagonality of the $2\times2$ Bhattacharyya matrices, J. Math. Sci. Inf., 1, (2), 73-78, 2006.
  20. Mohtashami Borzadaran, G. R., Rezaei Roknabadi, A. H. and Khorashadizadeh, M. A view on Bhattacharyya bounds for inverse Gaussian distributions, Metrika, 72, 2, 151-161, 2010.
  21. Nayeban, S., Rezaei Roknabadi, A. H. and Mohtashami Borzadaran, G. R. Bhattacharyya and Kshirsagar bounds in generalized gamma distribution, Communications in Statistics- Simulation and Computation, 42, 5, 969-980, 2013.
  22. Nayeban, S., Rezaei Roknabadi, A.H. and Mohtashami Borzadaran, G.R. Bhattacharrya and Kshirsagar Lower Bounds for the Natural Exponential Family (NEF), Economic Quality Control, 29, 1, 63-75, 2014.
  23. Patil, G. P. and Wani, J. K. Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic, Ann. Inst. Statist. Math. Tokyo 18, 39-47, 1966.
  24. Pommeret, D. Multidimensional Bhattacharyya matrices and exponential families, Journal of multivariate analysis, 63, 105-118, 1977.
  25. Pugh, E. L. The best estimate of reliability in the exponential case, Oper. Res. 11, 57-61, 1962.
  26. Qin, M. and Nayak, T. K. Kshirsagar-type lower bounds for mean squared error of prediction, Communications in Statistics - Theory and Methods, 37, 6, 861-872, 2008.
  27. Rao,C.R. Information and the accuracy attainable in the estimation of statistical parameters, Bull.Calcutta Math.Soc., 37,81-91, 1945.
  28. Shanbhag, D. N. Some characterizations based on the Bhattacharyya matrix, J. Appl. Probab., 9, 580-587, 1972.
  29. Shanbhag, D. N. Diagonality of the Bhattacharyya matrix as a characterization, Theory Probab. Appl., 24, 430-433, 1979.
  30. Tanaka, H. On a relation between a family of distributions attaining the Bhattacharyya bound and that of linear combinations of the distributions from an exponential family, Comm. Stat. Theory. Methods, 32, (10), 1885-1896, 2003.
  31. Tanaka, H. Location and scale parameter family of distributions attaining the Bhattacharyya bound, Communications in Statistics - Theory and Methods, 35, 9, 1611-1628, 2006.
  32. Tanaka, H. and Akahira, M. On a family of distributions attaining the Bhattacharyya bound, Ann. Inst. Stat. Math.,55, 309-317, 2003.
  33. Tong, H. A note on the estimation of $Pr(Y<X)$ in the exponential case, Technometrics, 16,4, 625-625, 1974.
  34. Tong, H. Errata: A note on the estimation of $Pr(Y<X)$ in the exponential case, Technometrics, 17, 395-395, 1975.
  35. Tsuda, Y., and Matsumoto, K. Quantum estimation for non-differentiable models, Journal of Physics A: Mathematical and General, 38, 7, 1593-1613, 2005.
  36. Zacks, S and Even, M. The efficiencies in small samples of the maximum likelihood and best unbiased estimators of reliability functions, Journal of the American Statistical Association, 61, 316, 1033-1051, 1966.