Abstract: | Suppose the multinomial parameters pr (θ) are functions of a real valued parameter 0, r = 1,2, …, k. A minimum discrepancy (m.d.) estimator θ of θ is defined as one which minimises the discrepancy function D = Σ nrf(pr/nr), for a suitable function f where nr is the relative frequency in r-th cell, r = 1,2, …, k. All the usual estimators like maximum likelihood (m. l), minimum chi-square (m. c. s.)., etc. are m.d. estimators. All m.d. estimators have the same asymptotic (first order) efficiency. They are compared on the basis of their deficiencies, a concept recently introduced by Hodges and Lehmann 2]. The expression for least deficiency at any θ is derived. It is shown that in general uniformly least deficient estimators do not exist. Necessary and sufficient conditions on pr (0) for m. t. and m. c. s. estimators to be uniformly least deficient are obtained. |