초록
In a multinomial sampling scheme some categories may be observed as partially classified because of technical or economic reasons. In this paper the maximum likelihood estimators(M.L.E) of multinomial probabilities are obtained when some frequencies are merged. We obtained the M.L.E and a method to evaluate the information gained by including merged frequencies in M.L.E we obtained an estimator of the covariance matrix and it is used to examine the information gained by including the merged frequency counts in estimating the cell probabilities. When certain individual frequency counts are missing a method is proposed for estimating the cell probabilities using EM algorithms.
