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

  • Carlos Martins-FilhoEmail author
  • Feng Yao


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.


U statistics V statistics local linear estimation 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2006

Authors and Affiliations

  1. 1.Department of EconomicsOregon State UniversityCorvallisUSA
  2. 2.Department of EconomicsUniversity of North DakotaGrand ForksUSA

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