Asymptotic Expansion and a Local Limit Theorem for a Function of the Kendall Rank Correlation Coefficient

Abstract

In the present paper, an integer-valued version $(T_N)$ of the Kendall rank correlation coefficient is considered. Under the hypothesis of independence, a local limit theorem with the Edgeworth expansion for $T_N$ is proved and an asymptotic expansion of the distribution function of $T_N$ is derived.