Order of magnitude bounds for expectations of Delta(2)-functions of generalized random bilinear forms

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 [GRAPHICS] 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).