### Abstract:

Consider the estimation of the category proportions in a
multinomial population from a sample which is "censored" in the
sense that under an appropriate, unknown permutation of the sample
categories, the population proportions are all known. We are considering
the estimation of an ordered set of sample proportions, known
except for their order. The estimation problem reduces to one of
matching a set of known sample proportions with a set of known
population proportions. The method of maximum likelihood yields
the matching that common sense or one's intuition would suggest;
highest sample proportion associated with highest population proportion,
second highest sample proportion with second highest population
proportion, and so forth. The work of this thesis is to
examine, by a complete enumeration of cases for some simple
problems, how good the method of maximum likelihood is. We
study the effectiveness of maximum likelihood matching under variation
of the three factors (1) "roughness" of the set of population proportions, (2) number of categories of the multinomial population,
and (3) size of the sample. The effectiveness of maximum likelihood
matching is measured by the ratio "proportion of the time
maximum likelihood matching correct" divided by "proportion of
the time random matching correct". The empirical study confirms
the conclusions suggested by intuition that: (1) the greater the
"roughness" of the set of population proportions, the more effective
is the method of maximum likelihood; (2) the greater the number of
categories the more effective is the method of maximum likelihood;
and (3) the greater the sample size the more effective is the method
of maximum likelihood.