Some Limit Theorems for the Indistinguishable Ball Problem with Applications in Nonparametrics.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Consider the following urn model, m urns and distribute n indistinguishable balls among the urns such that the distinguishable distributions of the balls all have the same probability. Let S sub K denote the number of balls in the Kth urn. Clearly S sub 1 ... S sub m n. In this paper, random variables of the type Z hS sub 1,...,S sub m, especially hS sub 1, ...,S sub m h sub 1 S sub 1 ... h sub m S sub m, are studied when m,n approaches the limit of infinity mn approaches the limit of rho, o rho infinity. Some applications of the results in nonparametric statistics are briefly discussed and the limit distribution of masS sub1,...,S sub m is derived.
- Statistics and Probability