On limiting distribution of U-statistics based on associated random variables

Abstract

Let {Xn,n≥1} be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on {Xn,n≥1} holds. We look at U-statistics based on differentiable kernels of degree 2 and above. As applications, we discuss consistent estimators of second, third and fourth central moments, and estimators of skewness and kurtosis based on them.