COMPARISON OF FOUR RATIO-TYPE ESTIMATES UNDER A MODEL.

In this paper, the simple estimate formed by the ratio of the sample means, the estimate obtained by the statistician M.H. Quenouille's method of bias reduction, the unbiased estimate of the statisticians L.A. Goodman and H.O. Hartley and the estimate proposed by H.O. Hartley are compared. These estimates are respectively denoted by t1, t2, t3 and t4. Mean square errors of these estimates are compared under J. Durbin's model. In practice g has often been found to lie between 0 and 2. In this paper expressions for the Mean Square Errors of these estimates are obtained for general values of n, g and h, and they are compared for finite values of n when g = 0, 1 and 2. When g = 0. The method of obtaining exact expressions for the Mean Square Errors (MSE's) of these estimates is similar to that of J.N.K. Rao and J.T. Webster. After a considerable amount of simplification, the following expressions for the biases and MSE's are obtained. When t=0, Durbin compared t1 with t2, and Rao compared t1 with t4.