NORMAL APPROXIMATION OF U-STATISTICS IN HILBERT SPACE
Yu. V. Borovskikh, L. MADAN PURI, V. V. SAZONOV · 2003
Let {Un}, n = 1, 2, . . ., be Hilbert space H-valued U -statistics with kernel Φ(• , •), corresponding to a sequence of observations (random variables) X 1 , X 2 , . . . .The rate of convergence on balls in the central limit theorem for {Un} is investigated.The obtained estimate is of order n -1/2 and depends explicitly on E Φ(X 1 , X 2 ) 3 and on the trace and the first nine eigenvalues of the covariance operator of E(Φ(X 1 , X 2 )|X 1 ).