Maximum likelihood estimation for the multinomial distribution with infinite number of cells
C. Radhakrishna Rao · 1958
SUMMARY. Maximum likelihood (m.l.) estimate of the infinite multinomial distribution exists with probability 1 and is consistent under a simple condition on the cell probabilities. To prove the consistency of an m.l. estimate of a parameter it is necessary to assume that the parameter is a continu ous function of the distribution. The existence of the m.l. estimates of parameters and their consis tency is established under conditions slightly weaker than those assumed by earlier writers. the problem of maximum likelihood estimation for the finite multinomial distribu tion (f.m.d.) to the case of a multinomial distribution with infinite number of cells, which may be denoted by (i.m.d.). As in the case of the f.m.d., the consistency of the maximum likelihood (m.l.) estimate of the i.m.d. is established first, and then the properties of m.l. equation esti mates are studied.