Mj. Klass et K. Nowicki, Order of magnitude bounds for expectations of Delta(2)-functions of generalized random bilinear forms, PROB TH REL, 112(4), 1998, pp. 457-492
Let Phi be a symmetric function, nondecreasing on [0, infinity) and satisfy
ing a Delta(2) growth condition, (X-1, Y-1), (X-2, Y-2), ..., (X-n,X- Y-n)
be arbitrary independent random vectors such that for any given i either Y-
i = X-i or Y-i is independent of ail the other variates. The purpose of thi
s paper is to develop an approximation of
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valid tor any constants {a(ij)}(1 less than or equal to i,j less than or eq
ual to n), {b(i)}(i=1)(n), {c(j)}(j=1)(n) and d. Our approach relies primar
ily on a chain of successive extensions of Khintchin's inequality for decou
pled random variables and the result of Klass and Nowicki (1997) for non-ne
gative bilinear forms of nonnegative random variables. The decoupling is ac
hieved by a slight modification of a theorem of de la Pena and Montgomery-S
mith (1995).