Abstract
We establish the \(\sqrt{n}\) 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 \(\sqrt{n}\) 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.
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Martins-Filho, C., Yao, F. A Note on the Use of V and U Statistics in Nonparametric Models of Regression. Ann Inst Stat Math 58, 389–406 (2006). https://doi.org/10.1007/s10463-006-0034-z
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DOI: https://doi.org/10.1007/s10463-006-0034-z