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Original Articles

On the Finite Sample Behavior of Fixed Bandwidth Bickel–Rosenblatt Test for Univariate and Multivariate Uniformity

Pages 827-846 | Received 19 May 2006, Accepted 19 Jan 2007, Published online: 25 Jun 2007

References

  • Anderson , E. , Bai , Z. , Bischof , C. , Blackford , S. , Demmel , J. , Dongarra , J. , Du Croz , J. , Greenbaum , A. , Hammarling , S. , McKenney , A. , Sorensen , D. ( 1999 ). LAPACK User's Guide. , 3rd ed. Philadelphia : SIAM .
  • Anderson , N.H. , Hall , P. , Titterington , D. M. ( 1994 ). Two sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates . J. Multivariate Anal. 50 : 41 – 54 .
  • Anderson , T.W. , Darling , D. A. ( 1954 ). A test of goodness of fit . J. Amer. Statist. Assoc. 49 : 765 – 769 .
  • Bickel , P. J. , Rosenblatt , M. ( 1973 ). On some global measures of the deviations of density function estimates . Ann. Statist. 1 : 1071 – 1095 .
  • Eubank , R. L. , LaRiccia , V. N. ( 1992 ). Asymptotic comparison of Crámer-von Mises and nonparametric function estimation techniques for testing goodness-of-fit . Ann. Statist. 20 : 2071 – 2086 .
  • Fan , Y. ( 1994 ). Testing the goodness of fit of a parametric density function by kernel method . Econometric Theor. 10 : 316 – 356 .
  • Fan , Y. (1998). Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters. Econometric Theor. 14:604–621.
  • Fang , H.-B. , Fang , K.-T. , Kotz , S. ( 2002 ). The meta-elliptical distributions with given marginals . J. Multivariate Anal. 82 : 1 – 16 .
  • Gouriéroux , C. , Tenreiro , C. ( 2001 ). Local power properties of kernel based goodness of fit tests . J. Multivariate Anal. 78 : 161 – 190 .
  • Gregory , G. G. ( 1977 ). Large sample theory for U-statistics and tests of fit . Ann. Statist. 5 : 110 – 123 .
  • Henze , N. ( 1997 ). Extreme smoothing and testing for multivariate normality . Statist. Probab. Lett. 35 : 203 – 213 .
  • Henze , N. , Wagner , T. ( 1997 ). A new approach to the BHEP tests for multivariate normality . J. Multivariate Anal. 62 : 1 – 23 .
  • Henze , N. , Zirkler , B. ( 1990 ). A class of invariante consistent tests for multivariate normality . Commun. Statist. Theor. Meth. 19 : 3595 – 3617 .
  • Johnson , M. E. ( 1987 ). Multivariate Statistical Simulation . New York : Wiley .
  • Kim , J.-T. ( 2000 ). An order selection criterion for testing goodness of fit . J. Amer. Statist. Assoc. 95 : 829 – 835 .
  • Koroljuk , V. S. , Borovskich , Yu. V. ( 1989 ). Theory of U-Statistics . Dordrecht : Kluwer .
  • Kotz , S. , Kozubowski , T. J. , Podgórski , K. ( 2000 ). An asymmetric multivariate Laplace distribution . Technical Report No. 367, Department of Statistics and Applied Probability, University of California at Santa Barbara .
  • Liang , J.-J. , Fang , K-T. , Hickernell , F. J. , Li , R. ( 2001 ). Testing multivariate uniformity and its applications . Math. Comp. 70 : 337 – 355 .
  • Madras , N. ( 2002 ). Lectures on Monte Carlo Methods . Providence , RI : AMS .
  • Marhuenda , Y. , Morales , D. , Pardo , M. C. ( 2005 ). A comparison of uniformity tests . Statistics 39 : 315 – 328 .
  • Miller , F. L.jun. , Quesenberry , C. P. ( 1979 ). Power studies of tests for uniformity. II . Commun. Statist. Simul. Comput. B 8 : 271 – 290 .
  • Nikitin , Y. ( 1995 ). Asymptotic Efficiency of Nonparametric Tests . Cambridge : Cambridge University Press .
  • Parzen , E. ( 1962 ). On estimation of a probability density function and mode . Ann. Math. Statist. 33 : 1065 – 1076 .
  • Rosenblatt , M. ( 1952 ). Remarks on a multivariate transformation . Ann. Math. Statist. 23 : 470 – 472 .
  • Rosenblatt , M. ( 1956 ). Remarks on some non-parametric estimates of a density function . Ann. Math. Statist. 27 : 832 – 837 .
  • Shorack , G. R. , Wellner , J. A. ( 1986 ). Empirical Processes with Applications to Statistics . New York : Wiley .
  • Stephens , M. A. ( 1974 ). EDF statistics for goodness of fit and some comparisons . J. Amer. Statist. Assoc. 69 : 730 – 737 .
  • Stephens , M. A. ( 1986 ). Tests for the uniform distribution . In: D'Agostino , R. B. , Stephens , M. A. , eds. Goodness-of-Fit Techniques . New York : Marcel Dekker , pp. 331 – 366 .
  • Tenreiro , C. ( 2005 ). On the role played by the fixed bandwidth in the Bickel–Rosenblatt goodness-of-fit test . SORT 29 : 201 – 216 .
  • Tenreiro , C. ( 2007 ). On the asymptotic behaviour of location-scale invariant Bickel–Rosenblatt tests . J. Statist. Plann. Inf. 137 : 103 – 116 .
  • Watson , G. S. ( 1961 ). Goodness-of-fit tests on a circle . Biometrika 48 : 109 – 114 .

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