... a 2 = ai, while for 0 2 = ai, ~ is maximized at K == Y l • On the other hand if HM,ai,y l ) > ~(M,a~'Yl) then for any value of K < Y l , the minimum of ~(M,a2,K) with respect to a2 must be less than =-=(2)-=-. (2) ~ M,crO'Y l due to the fact that both ~ M,aO,K and 2 ~(M,al,K) decrease as K decreases from K = Y l • For Y l .:: K ~ YO' HM,(J~,K) will be strictly increasing, while 2 ~(M,crl,K) will be strict...

...pondence between confidence intervals and (two-sided) tests, where our estimator can be 4 thought of as defining the center of a confidence interval for e of width 2g. Following Dantzig's work, Stein =-=(3)-=- developed a two sample sequential procedure for establishing fixed width confidence intervals independent of 0 2 , at prescribed a levels. Since we wish our closeness measure to be as large as possib...

... of K, probability deviations, and BLUE probabilities for Type B estimator -- O' 2 e;[. 03, .07] · · 67 7.23. Values of K, probability deviations, and BLUE probabilities for Type B estimator -- O' 2 €=-=[1, 10]-=- . . · · 68 7.24. Values of K, probability deviations, and BLUE probabilities for Type B estimator __ O' 2€[10, 20] 69 7.25. 7.26. Percent increase in probability over minimum BLUE probability for Typ...

...olically: We will proceed by first considering the single 8 case, for two different formulations of the problem, and finally extending the results to the general p 8 case. 1.2 First Procedure Webster =-=[4]-=- considered this criterion, and referred to it as an "e:-neighbot,lrhood" criterion. A He considers ).11 better than ).12 ~or estimating V if, for fixed e:: Webster compares two estimators, Xl and X 2...