¹Yazd University, Department of Statistics, Yazd, Iran. Assistant Professor. Email: hzaker@yazd.ac.ir
²Yazd University, Department of Statistics, Yazd, Iran. Assistant Professor. Email: aajafari@yazd.ac.ir
³Yazd University, Department of Statistics, Yazd, Iran. Student. Email: mkarimiz68@yahoo.com

This paper studies shrinkage estimation after the preliminary test for the parameters of exponential distribution based on record values. The optimal value of shrinkage coefficients is also obtained based on the minimax regret criterion. The maximum likelihood, pre-test, and shrinkage estimators are compared using a simulation study. The results to estimate the scale parameter show that the optimal shrinkage estimator is better than the maximum likelihood estimator in all cases, and when the prior guess is near the true value, the pre-test estimator is better than shrinkage estimator. The results to estimate the location parameter show that the optimal shrinkage estimator is better than maximum likelihood estimator when a prior guess is close to the true value. All estimators are illustrated by a numerical example.

Key words: Exponential Distribution, Minimax Regret, Record Value, Risk Function, Shrinkage Estimator.

Este artículo estudia la estimación shrinkage posterior al test preliminar de los parámetros de la distribución exponencial basada en valores record. El valor óptimo de los coeficientes de shrinkage es obtenido también usando el criterio minimax regret. La máxima verosimilitud, pre-test, y los estimadores shrinkage son obtenidos usando estudios de simulación. Los resultados de la estimación del parámetro de escala muestran que el estimador shrinkage es major que el de máxima verosimilitud en todos los casos, y cuando el valor a priori es cercano del valor real, el estimador pre-test es major que el estimador shrinkage. Los resultados de estimación del parámetro de localización muestran que el estimador de shrinkage óptimo es major que el de máxima verosimilitud cuando el valor a priori es cercano al real. Todos los estimadores son ilustrados con un ejemplo numérico.

Palabras clave: estimador shrinkage, distribución exponencial, minimax regret, función de riesgo, valor record.

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References

1. Ahsanullah, M. (1995), Record statistics, Nova Science Publishers Commack, New York.         [ Links ]

2. Arnold, B., Balakrishnan, N. & Nagaraja, H. (1998), Records, John Wiley & Sons Inc, New York.         [ Links ]

3. Balakrishnan, N. & Chan, P. S. (1994), 'Record values from Rayleigh and Weibull distributions and associated inference', National Institute of Standards and Technology Journal of Research, Special Publication, Proceedings of the Conference on Extreme Value Theory and Applications 866, 41-51.         [ Links ]

4. Bancroft, T. A. (1944), 'On biases in estimation due to the use of preliminary tests of significance', The Annals of Mathematical Statistics 15(2), 190-204.         [ Links ]

5. Bancroft, T. A. & Han, C. P. (1977), 'Inference based on conditional specification: a note and a bibliography', International Statistical Review 45, 117-127.         [ Links ]

6. Bhattacharya, S. K. & Srivastava, V. K. (1974), 'A preliminary test procedure in life testing', Journal of the American Statistical Association 69(347), 726-729.         [ Links ]

7. Chiou, P. (1990), 'Estimation of scale parameters for two exponential distributions', IEEE Transactions on Reliability 39(1), 106-109.         [ Links ]

8. Chiou, P. & Han, C. P. (1995), 'Conditional interval estimation of the exponential location parameter following rejection of a pre-test', Communications in Statistics-Theory and Methods 24(6), 1481-1492.         [ Links ]

9. Chiou, P. & Han, C. (1989), 'Shrinkage estimation of threshold parameter of the exponential distribution', IEEE transactions on reliability 38, 449-453.         [ Links ]

10. Chiou, P. & Miao, W. (2005), 'Shrinkage estimation for the difference between exponential guarantee time parameters', Computational Statistics and Data Analysis 48(3), 489-507.         [ Links ]

11. Dunsmore, I. R. (1983), 'The future occurrence of records', Annals of the Institute of Statistical Mathematics 35(1), 267-277.         [ Links ]

12. Han, Chien-Pai, Rao, C. & Ravichandran, J. (1988), 'Inference based on conditional speclfication', Communications in Statistics-Theory and Methods 17(6), 1945-1964.         [ Links ]

13. Inada, K. (1984), 'A minimax regret estimator of a normal mean after preliminary test', Annals of the Institute of Statistical Mathematics 36(1), 207-215.         [ Links ]

14. Pandey, B. N. (1983), 'Shrinkage estimation of the exponential scale parameter', IEEE Transactions on Reliability 32(2), 203-205.         [ Links ]

15. Pandey, B. N. (1997), 'Testimator of the scale parameter of the exponential distribution using LINEX loss function', Communications in Statistics-Theory and Methods 26(9), 2191-2202.         [ Links ]

16. Prakash, G. & Singh, D. (2008), 'Shrinkage estimation in exponential type-II censored data under LINEX loss', Journal of the Korean Statistical Society 37(1), 53-61.         [ Links ]

17. Zakerzadeh, H. & Karimi, M. (2013), Preliminary test estimation of exponential distribution based on record values, 'The 9th Seminar on Probability and Stochastic Processes, Iran, Zahedan'.         [ Links ]

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