Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Negative Exponential Disparity Based Deviance and Goodness-of-fit Tests for Continuous Models: Distributions, Efficiency and Robustness

  • Jeong, Dong-Bin (Department of Statistics, Kangnung National University) ;
  • Sahadeb Sarkar (O.M. Group, Indian Institute of Management Calcutta)
  • Published : 2001.03.01
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Abstract

The minimum negative exponential disparity estimator(MNEDE), introduced by Lindsay(1994), is an excellenet competitor to the minimum Hellinger distance estimator(Beran 1977) as a robust and yet efficient alternative to the maximum likelihood estimator in parametric models. In this paper we define the negative exponential deviance test(NEDT) as an analog of the likelihood ratio test(LRT), and show that the NEDT is asymptotically equivalent to he LRT at the model and under a sequence of contiguous alternatives. We establish that the asymptotic strong breakdown point for a class of minimum disparity estimators, containing the MNEDE, is at least 1/2 in continuous models. This result leads us to anticipate robustness of the NEDT under data contamination, and we demonstrate it empirically. In fact, in the simulation settings considered here the empirical level of the NEDT show more stability than the Hellinger deviance test(Simpson 1989). The NEDT is illustrated through an example data set. We also define a goodness-of-fit statistic to assess adequacy of a specified parametric model, and establish its asymptotic normality under the null hypothesis.

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