A test of goodness-of -fit based on extreme multinomial cell frequencies

Abstract

For the problem of testing goodness-of-fit of a specified distribution, a new test based on the number of extreme cell frequencies is proposed. A cell is called "sparse" ("crowded") if the corresponding cell frequency is less than (greater than) or equal to a value u ≥ 0(v ≥ 0). Then, the proposed test statistic , is the number of sparse plus croweded, cells, where n denotes the sample and N is the number of mutually exclusive and collectively exhaustive cells. The exact distribution of is derived under the null hypothesis. The asymptotic distribution of under a sequence of local alternatives is also derived. The efficiency of this test statistic with respect to several other test statistics is obtained. A discussion of the merits and shortcomings of the proposed test procedure is also given.

Keywords:

• sparse cells
• crowded cells
• spacings
• asymptotic normality
• efficiency