Communications for Statistical Applications and Methods

  • 제5권2호
  • /
  • Pages.517-529
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  • 1998
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

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)
  • 발행 : 1998.08.01
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초록

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.

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참고문헌

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