A note on the use of V and U statistics in nonparametric models of regression
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چکیده
We establish the √ 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 √ 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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تاریخ انتشار 2006