Negative exponential disparity based family of goodness-of-fit tests for multinomial models
This paper investigates a new family of goodness-of-fit tests based on the negative exponential disparities. This family includes the popular Pearson's chi-square as a member and is a subclass of the general class of disparity tests (Basu and Sarkar, 1994) which also contains the family of power divergence statistics. Pitman efficiency and finite sample power comparisons between different members of this new family are made. Three asymptotic approximations of the exact null distributions of the negative exponential disparity family of tests are discussed. Some numerical results on the small sample performance of this family of tests are presented for the symmetric null hypothesis. It is shown that the negative exponential disparity family, like the power divergence family, produces a new goodness-of-fit test statistic that can be a very attractive alternative to the Pearson's chi-square. Some numerical results suggest that, application of this test statistic, as an alternative to Pearson's chi-square, could be preferable to the I-2/3 statistic of Cressie and Read (1984) under the use of chi-square critical values.
negative exponential disparity goodness-of-fit pearson's chi-square disparity tests power divergence likelihood ratio test