Statistics & Probability Letters 57 (2002) 9–15 Central limit theorem for U-statistics of associated random variables Isha Dewan ∗ , B.L.S. Prakasa Rao Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India Received May 2001; received in revised form September 2001 Abstract Let {X n ;n ¿ 1} be a sequence of stationary associated random variables. Let U n be a U-statistic based on this sample. We establish the Central Limit Theorem for U n using the Hoeding’s decomposition. c  2002 Published by Elsevier Science B.V. Keywords: U-statistics; Central limit theorem; Associated random variables 1. Introduction Let {X n ;n ¿ 1} be a sequence of stationary associated random variables, that is, for every k and for every pair of functions h(x) and g(x) from R k to R; k ¿ 1, which are non-decreasing componentwise, Cov(h(X); g(X)) ¿ 0 whenever it is nite, where X =(X 1 ;X 2 ;:::;X k ) (cf. Esary et al., 1967). Let F be the distribution function of X 1 and f be its density function, assuming that the random variable X 1 has a probability density function. Associated random variables are of considerable interest in reliability studies, percolation theory and statistical mechanics. For a review of several probabilistic and statistical inferential results for associated sequences, see Prakasa Rao and Dewan (2001) and Roussas (1999). Let  (x;y) be a real-valued function symmetric in its arguments. Dene the U-statistic by U n =  n 2  -1  16i¡j6n  (X i ;X j ): (1.1) * Corresponding author. E-mail address: isha@isid.ac.in (I. Dewan). 0167-7152/02/$-see front matter c  2002 Published by Elsevier Science B.V. PII:S0167-7152(01)00194-8