By F. Gravetter, L. Wallnau

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N 2nBE)'[I - Bk(B B )-I B,] (d - n2nnBkE) and k n k k k k k k 1 ! k - n 2nBE)'L n k k -I (d ! 2 of Moore and Spruill (1975). Let w and w be the kl k2 eigenvectors of ILk with eigenvalues ~I and ~2 and let vj = wkj(d k - n2nnBkE) (j = 1,2). 9) WR (2. 1O) (2. II) k k din ,2 (6RR) Xk - I k • /~I) + ~2xi2 2 (vzl~2) , F. C. DROST 48 Let k As under H , the limiting alternative distributions are the a first order approximations of the limiting distributions for fixed k ~ 00 (cf. 1). 1). As a consequence of Theorem 4.

Of Statistics·13, 1465-1482. A. (1962). Some limit theorem for stationary processes, Thpory Probe Appl. 7, 349-382. , Theodorescu, R. (1969). Springer-Verlag. Nadaraja, E. (1964). 9, 157-159. Random Processes and Learning, On regression estimators, Theory Probab. Appl. Parzen, E. (1962). On estimation of a probability density function and mode, Ann. Math. Statist. 33, 1065-1076. Peligrad, M. (1986). Properties of uniform consistency of the kernel estimator of a density and of a regression function under dependence assumptions.

R. NEDELJKOVIC Proof. It is obvious that m~n L(R,T) ~ L(O,OQ) = c + dim, and, from (3), e/(m+R), m~n L(R,T) ~ e/T. But, min LCR,T) ~ mintLCO,oo),LCoo,e>e»! = min {c + d/m,a}. Now R,T e/(m+R o ) ~ min Ic + d/m,a}, e/T o ~ min~c + d/m,a} give the resu Lt. 4. APPLICATION TO THE EXPONENTIAL LIFE DISTRIBUTION Let F(x) = 1 - exp(-x/m), x~O. Theorem 4. The optimaL strategy is (OQ,oo) if and onLy if a ~ min{b/m, c + dim}. Proof. The strategy (00,00) is the best one if and onLy if L(R,T) ~ ~ L(oo,oo) = a, for aLL Rand T, which is equivaLent to the inequaLi ty: (c-a)S:(1-F(x»dx - cS:(1-F(X»dX + (b-d)F(R) + + (d-e)F(T) + e ~ O.

### Statistics for the Behavioral Sciences [Int'l Student ed.] by F. Gravetter, L. Wallnau

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