Non-Gaussian limit distributions for U -statistics based on trimmed and Winsorized samples.

Conditions ensuring the asymptotic normality ofU-statistics based on either trimmed samples or Winsorized samples are well known [P. Janssen, R. Serfling, and N. Veraverbeke,Asymptotic normality of U-statistics based on trimmed samples, J. Statist. Plann. Inference 16 (1987), pp. 63–74;U-statistics on Winsorized and trimmed samples, Statist. Probab. Lett. 9 (1990), pp. 439–447]. However, the class ofU-statistics has a much richer family of limiting distributions. This paper complements known results by providing general limit theorems forU-statistics based on trimmed or Winsorized samples where the limiting distribution is given in terms of multiple Ito–Wiener stochastic integrals. [ABSTRACT FROM AUTHOR]