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Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

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Abstract

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.

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References

  • Basu, A. and Lindsay, B. G. (1994). Minimum disparity estimation for continuous models: efficiency, distributions and robustness, Ann. Inst. Statist. Math., 46, 683–705.

    Google Scholar 

  • Beran, R. J. (1977). Minimum Hellinger distance estimates for parametric models, Ann. Statist., 5, 445–463.

    Google Scholar 

  • Chung, K. L. (1974). A Course in Probability Theory, Academic Press, New York.

    Google Scholar 

  • Chow, Y. S. and Teicher, H. (1988). Probability Theory; Independence, Interchangeability, Martingales, 2nd ed., Springer, New York.

    Google Scholar 

  • Cressie, N. and Read, T. R. C. (1984). Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B, 46, 440–464.

    Google Scholar 

  • Lehmann, E. L. (1991). Theory of Point Estimation, Wiley, New York.

    Google Scholar 

  • Lindsay, B. G. (1994). Efficiency versus robustness: the case for minimum Hellinger distance and related methods, Ann. Statist., 22, 1081–1114.

    Google Scholar 

  • Pak, Ro Jin (1995). Robustness of minimum disparity estimation in linear regression models, Journal of Korean Statistical Association, 24, 349–360.

    Google Scholar 

  • Pak, Ro Jin (1996). Minimum Hellinger distance estimation in simple linear regression models; distribution and efficiency, Statist. Probab. Lett., 26, 263–269.

    Google Scholar 

  • Rao, C. R. (1961). Asvmptotic efficiency and limiting information, Proceedings of the Fourth Berkeley Symposium, Vol. 1, 531–546, University of California Press, Berkeley.

    Google Scholar 

  • Rousseeuw, P. J. and Leroy, A. (1987). Robust Regression and Outlier Detection, Wiley, New York.

    Google Scholar 

  • Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York.

    Google Scholar 

  • Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data, J. Amer. Statist. Assoc., 82, 802–807.

    Google Scholar 

  • Tamura, R. N. and Boos, D. D. (1986). Minimum Hellinger distance estimation for multivariate location and covariance, J. Amer. Statist. Assoc., 81, 223–229.

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Taejon University, Taejon, 300-716, Korea

    Ro Jin Pak

  2. Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta, 700 035, India

    Ayanendranath Basu

Authors
  1. Ro Jin Pak
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  2. Ayanendranath Basu
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Pak, R.J., Basu, A. Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency. Annals of the Institute of Statistical Mathematics 50, 503–521 (1998). https://doi.org/10.1023/A:1003577412390

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  • DOI: https://doi.org/10.1023/A:1003577412390

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