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Original Articles

The central limit theorem for degenerate variable U-statistics under dependence

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Pages 683-699 | Received 12 Jul 2010, Accepted 15 Jan 2011, Published online: 19 Apr 2011

References

  • De Jong , P. 1987 . A Central Limit Theorems for Generalized Quadratic Form . Probability Theory and Related Fields , 75 : 261 – 277 .
  • Eubank , R. L. and Wang , S. 1999 . A Central Limit Theorem for the Sum of Generalized Linear and Quadratic Forms . Statistics , 33 ( 1 ) : 85 – 91 .
  • Fan , J. and Li , Q. 1996 . Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms . Econometrica , 64 : 865 – 890 .
  • Fan , J. and Li , Q. 1999 . Central Limit Theorem for Degenerate U-Statistics of Absolutely Regular Processes with Applications to Model Specification Testing . Journal of Nonparametric Statistics , 10 : 245 – 271 .
  • Francq , C. and Zakoïan , J. 2005 . A Central Limit Theorem for Mixing Triangular Arrays of Variables Whose Dependence is Allowed to Grow with the Sample Size . Econometric Theory , 21 : 1165 – 1171 .
  • Gao , J. 2007 . Nonlinear Time Series: Semiparametric and Nonparametric Methods , London : Chapman & Hall/CRC .
  • Gao , J. and Hong , Y. 2008 . Central Limit Theorem for Generalized U-Statistics with Applications in Nonparametric Specification . Journal of Nonparametric Statistics , 20 : 61 – 76 .
  • Gao , J. and King , M. L. 2004 . Adaptive Testing in Continuous-time Diffusion Models . Econometric Theory , 20 : 844 – 882 .
  • Gyöfri , L. , Härdle , W. , Sarda , P. and Vieu , P. 1990 . Nonparametric Curve Estimation from Time Series , New York/Berlin : Springer-Verlag . Lecture Notes in Statistics 60
  • Hall , P. 1984 . Central Limit Theorem for Integrated Square Error of Multivariate Nonparametric Density Estimators . Journal of Multivariate Analysis , 14 : 1 – 16 .
  • Kashimov , S. A. 1987 . On the Asymptotic Distribution of the Generalized U-Statistics for Dependent Variables . Theory of Probability and its Applications , 32 : 373 – 375 .
  • Kashimov , S. A. 1992 . Limiting Behavior of Generalized U-Statistics of Weakly Dependent Stationary Processes . Theory of Probability and its Applications , 37 : 148 – 150 .
  • Kim , T. Y. and Cox , D. D. 1995 . Asymptotic Behavior of Some Measures of Accuracy in Nonparametric Curve Estimation with Dependent Observations . Journal of Multivariate Analysis , 53 : 67 – 93 .
  • Kim , T. Y. and Cox , D. D. 2001 . Convergence Rates for Average Square Errors for Kernel Smoothing Estimators . Journal of Nonparametric Statistics , 13 : 209 – 228 .
  • Lee , S. and Na , S. 2000 . A Nonparametric Goodness of Fit Test for Strong Mixing Processes . Annales de L'I.S.U.P. , 44 : 3 – 20 .
  • Robinson , P. M. 1983 . Nonparametric Estimators for Time Series . Journal of Time Series Analysis , 4 : 185 – 207 .
  • Roussas , G. G. and Ioannides , D. 1987 . Moment Inequalities for Mixing Sequences of Random Variables . Stochastic Analysis and Applications , 5 : 61 – 120 .
  • Takahata , H. and Yoshihara , K. 1987 . Central Limit Theorems for Integrated Square Error of Nonparametric Density Estimators Based on a Absolutely Regular Random Sequences . Yokohama Mathematical Journal , 35 : 95 – 111 .
  • Yoshihara , K. 1989 . Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences II . Yokohama Mathematical Journal , 37 : 109 – 123 .
  • Yoshihara , K. 1992 . Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences III . Yokohama Mathematical Journal , 40 : 1 – 9 .

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