Sample Size, Parameter Rates And Contiguity-T1 Ie I. I. D. Case

Let X,*., X be i.i.d. r. v.'s defined on the _{r ct}probability space (X. A, P _), where 0 £0 is an open sub~ k ° set of 3R, k1 ; (ocl, n1, is a nondecreasiny sequence n of positive integers tending to ₀₀ as Let {x}, n1, be a sequence of positive real numbers tending to ₀₀ as n°°, and set 0_T=0+h 1, h£3R, hO. Finally, let P_aQ ‘ n n _{1 n}, 0 ry-jj _{f and}P ‘ be the restrictions of the urobability measu-n, 0 p _{1 res} P_Q and P_pt, respectively, to the a-fie1d A - an ‘n a(X,…, X)„ Then a necessary and sufficient condiantion for the sequences {P _Q} and {P ‘ } to be contin,0 n,0 guous is that _an=0(x), provided certain fairly mild conditions are satisfied. Copyright.