A Note on the Use of V and U Statistics in Nonparametric Models of Regression

We establish the asymptotic equivalence of V and U statistics when the statistic’s kernel depends on n. Combined with a lemma of B. Lee this result provides conditions under which U statistics projections and V statistics are asymptotically equivalent. The use of this equivalence in nonparametric regression models is illustrated with several examples; the estimation of conditional variances, skewness, kurtosis and the construction of a nonparametric R-squared measure.