Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Minimum Disparity Estimation for Normal Models: Small Sample Efficiency

  • Cho M. J. (Research Institute of Applied Statistics, Sungkyunkwan University) ;
  • Hong C. S. (Department of Statistics, Sungkyunkwan University) ;
  • Jeong D. B. (Department of Information Statistics, Kangnung National University)
  • Published : 2005.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

The minimum disparity estimators introduced by Lindsay and Basu (1994) are studied empirically. An extensive simulation in this paper provides a location estimate of the small sample and supplies empirical evidence of the estimator performance for the univariate contaminated normal model. Empirical results show that the minimum generalized negative exponential disparity estimator (MGNEDE) obtains high efficiency for small sample sizes and dominates the maximum likelihood estimator (MLE) and the minimum blended weight Hellinger distance estimator (MBWHDE) with respect to efficiency at the contaminated model.

Keywords

References

  1. Basu, A. and Lindsay, B. G. (1994). Minimum disparity estimation for continuous models: efficiency, distributions and robustness, Annals of the Institute of Statistical Mathematics, Vol. 46, 683-705 https://doi.org/10.1007/BF00773476
  2. Basu, A. and Sarkar, S. (1994a). The Trade-Off Between Robustness and Efficiency and The Effect of Model Smoothing in Minimum Disparity inference, Journal of Statistical Computation and Simulation, Vol. 50, 173-185 https://doi.org/10.1080/00949659408811609
  3. Basu, A. and Sarkar, S. (1994b). Minimum disparity estimation in the errors-in-variables model, Statistics & Probability Letter, Vol. 20, 69-73 https://doi.org/10.1016/0167-7152(94)90236-4
  4. Basu, A. Sarkar, S. and Vidyashankar, A. N. (1997). Minimum negative exponential disparity estimation in parametric models, Journal of Statistical Planning and Irference, Vol. 58, 349-370 https://doi.org/10.1016/S0378-3758(96)00078-X
  5. Beran, R. J. (1977). Minimum Hellinger distance estimates for parametric models, Annals of Statistics, Vol. 5, 445-463 https://doi.org/10.1214/aos/1176343842
  6. Cressie, N. and Read, T. (1984). Multinomial Goodness-of-fit Tests, Journal of the Royal Statistical Society B, Vol. 46, No.3, 440-464
  7. Csiszar, I. (1963). Eine informations theoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten. Publ. Math Inst. Hungar. Acad Sci., Vol. 3, 85-107
  8. Devroye, L. and Gyorfi, L. (1985). Nonparametric Density Estimation: The $L_1$ View, John Wiley, New York
  9. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Irfluence Functions, John Wiley, New York
  10. Jeong, D. B. and Sarkar, S. (2001). Negative Exponential Disparity Based Deviance and Goodness-of-fit Tests for Continuous Models: Distribution, Efficiency and Robustness, Journal of the Korean Statistical Society, Vol. 30: 1, 41-61
  11. Jeong, D. B. and Sarkar, S. (2000). Negative exponential disparity family based goodness-of-fit tests for multinomial models. Journal of Statistical Computation and Simulation, Vol. 65, 43-61 https://doi.org/10.1080/00949650008811989
  12. Lindsay, B. G. (1994). Efficiency versus robustness: The case for minimum Hellinger distance and related methods, Annals of Statistics, Vol. 22, 1081-1114 https://doi.org/10.1214/aos/1176325512
  13. Parzen, E. (1962), On estimation of a probability density function and its mode, Annals of Mathematical Statistics, Vol. 33, 1065-1076 https://doi.org/10.1214/aoms/1177704472
  14. Sarkar, S., Basu, A. and Shin, D. W. (1996). Small sample comparisons for the blended weight chi-square goodness-of-fit test statistics. Communications in Statistics, Theory and Method, Vol. 25, 211-226 https://doi.org/10.1080/03610929608831689
  15. Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data, Journal of the American Statistical Association, Vol. 82, 802-807 https://doi.org/10.2307/2288789
  16. Simpson, D. G. (1989). Hellinger Deviance Tests: Efficiency, Breakdown Points, and Examples, Journal of the American Statistical Association, Vol. 84, 107-113 https://doi.org/10.2307/2289852
  17. Stather, C. R. (1981). Robust Statistical Inference using Hellinger Distance Methods, Unpublished Ph. D. Dissertation, La Trobe University, Melbourne, Australia
  18. Tamura, R. N. and Boos, D. D. (1986). Minimum Hellinger Distance Estimation for Multivariate Location and Covariance, Journal of the American Statistical Association, Vol. 81, 223-229 https://doi.org/10.2307/2287994