On Constructing Confidence Intervals for Functions of a Multinomial Parameter,
DEPARTMENT OF JUSTICE WASHINGTON DC
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We consider the problem of constructing confidence intervals for possibly messy functions of a multinomial parameter. The number of categories can be large and the sample size small, meaning that the problem of sparseness must be confronted. Thus, standard asymptotics based on the delta method will often prove unsatisfactory. Alternatives to the delta method include 1 Madanskys method, based on constrained maximum likelihood 2 the bootstrap and 3 intervals derived from the brute force Monte Carlo calculation of exact confidence regions. These approaches are discussed and contrasted in the context of an empirical problem.
- Statistics and Probability