This research aims for testing of homogeneity against the umbrella alternatives in multinomial population. There are lots of literlatures of testing homogeneity against the omnibus alternatives, but no research has been done for this area so far. Sinc...
This research aims for testing of homogeneity against the umbrella alternatives in multinomial population. There are lots of literlatures of testing homogeneity against the omnibus alternatives, but no research has been done for this area so far. Since this umbrella alternative is very practical in social science fields, we will consider several testing procedures about it.
First, we construct the likelihood ratio test for this problem using isotonic regression ideas in the case that the peak point is known. Second, we will obtain the maximin test for this case and then compare this with the likelihood ratio test via simulation studies.