Penalizing the Negative Exponential Disparity in Discrete Models

  • Sahadeb Sarkar (Department of Statistics, Oklahoma State University) ;
  • Song, Kijoung-Song (Department of Epidemiology and Biostatistics, Case western reserve University) ;
  • Jeong, Dong-Bin (Department of Statistics, Kangnung National University)
  • Published : 1998.08.01


When the sample size is small the robust minimum Hellinger distance (HD) estimator can have substantially poor relative efficiency at the true model. Similarly, approximating the exact null distributions of the ordinary Hellinger distance tests with the limiting chi-square distributions can be quite inappropriate in small samples. To overcome these problems Harris and Basu (1994) and Basu et at. (1996) recommended using a modified HD called penalized Hellinger distance (PHD). Lindsay (1994) and Basu et al. (1997) showed that another density based distance, namely the negative exponential disparity (NED), is a major competitor to the Hellinger distance in producing an asymptotically fully efficient and robust estimator. In this paper we investigate the small sample performance of the estimates and tests based on the NED and penalized NED (PNED). Our results indicate that, in the settings considered here, the NED, unlike the HD, produces estimators that perform very well in small samples and penalizing the NED does not help. However, in testing of hypotheses, the deviance test based on a PNED appears to achieve the best small-sample level compared to tests based on the NED, HD and PHD.



  1. Statist. Prob. Letters v.27 Tests of hypotheses in discrete models based on the penalized Hellinger distance Basu, A.;Harris, I. R.;Basu, S.
  2. Ann. Inst. Statist. Math. v.46 Minimum disparity estimation for continuous models: Efficiency, distributions and robustness Basu, A.;Lindsay, B. G.
  3. J. Statist. Comput. Simul. v.50 The trade-off between robustness and efficiency and the effect of model smoothing in minimum disparity inference Basu, A.;Sarkar, S.
  4. Journal of Statistical Planning and Inference v.58 Minimum negative exponential disparity estimation in parametric models Basu, A.;Sarkar, S.;Vidyashankar, A. N.
  5. Ann. Statist. v.5 Minimum Hellinger distance estimates for parametric models Beran, R.
  6. Commun. Statist. Simula v.23 no.4 Hellinger distance as a penalized log likelihood Harris, I. R.;Basu, A.
  7. Ann. Math. Statist. v.22 On information and sufficiency Kullback, S.;Leibler, R. A.
  8. Ann. Statist. v.22 Efficiency versus robustness: the case of minimum Hellinger distance and related methods Lindsay, B. G.
  9. Commun. Statist. Simula v.24 Robust minimum distance inference based on combined distances Park, C.;Basu, A.;Basu, S.
  10. J. Amer. Statist. Assoc. v.82 Minimum Hellinger distance estimation for the analysis of count data Simpson, D. G.
  11. J. Amer. Statist. Assoc. v.84 Hellinger deviance test: efficiency, breakdown points, and examples Simpson, D. G.
  12. J. Amer. Statist. Assoc. v.81 Minimum Hellinger distance estimation for multivariate location and covariance Tamura, R. N.;D. D. Boos