On the choice of the smoothing parameter for the BHEP goodness-of-fit test

Computational Statistics and Data Analysis

Volumn 53, Issue 4, 2009, Pages 1038-1053

  Tenreiro, Carlos ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

GAIT ANALYSIS; IMAGE SEGMENTATION;

COMPARATIVE STUDIES; MONTE CARLO STUDY; TEST PROCEDURES; UNIVARIATE; WIDE-RANGE;

TESTING;

EID: 58549112762     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.09.002     Document Type: Article

References (35)

1. Anderson N.H., Hall P., and Titterington D.M. Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates. J. Multivariate Anal. 50 (1994) 41-54
2. Arcones M.A. On the Bahadur slope of the Lilliefors and the Cramér-von Mises tests of normality. In: Giné E., Koltchinskii V., Li W., and Zinn J. (Eds). IMS Lecture Notes - High Dimensional Probability vol. 51 (2006) 196-206
3. Arcones M.A., and Wang Y. Some new tests for normality based on U-processes. Statist. Probab. Lett. 76 (2006) 69-82
4. Arcones M.A. Two tests for multivariate normality based on the characteristic function. Math. Methods Statist. 16 (2007) 177-201
5. Bahadur R.R. Stochastic comparison of tests. Ann. Math. Statist. 31 (1960) 276-295
6. Bahadur R.R. Rates of convergence of estimates and test statistics. Ann. Math. Statist. 38 (1967) 303-324
7. Bahadur R.R. Some Limit Theorems in Statistics (1971), SIAM, Philadelphia
8. Baringhaus L., and Henze N. A consistent test for multivariate normality based on the empirical characteristic function. Metrika 35 (1988) 339-348
9. Baringhaus L., Danschke R., and Henze N. Recent and classical tests for normality. A comparative study. Comm. Statist. Simulation Comput. 18 (1989) 363-379
10. Bickel P.J., and Rosenblatt M. On some global measures of the deviations of density function estimates. Ann. Statist. 1 (1973) 1071-1095
11. Bowman A.W., and Foster P.J. Adaptive smoothing and density-based tests of multivariate normality. J. Amer. Statist. Assoc. 88 (1993) 529-537
12. Coin D. A goodness-of-fit test for normality based on polynomial regression. Comput. Statist. Data Anal. 52 (2008) 2185-2198
13. Csörgo{double acute} S. Consistency of some tests for multivariate normality. Metrika 36 (1989) 107-116
14. Durbin J., Knott M., and Taylor C.C. Components of Cramér-von Mises Statistics, II. J. Roy. Statist. Soc. Ser. B 37 (1975) 216-237
15. Epps T.W., and Pulley L.B. A test for normality based on the empirical characteristic function. Biometrika 70 (1983) 723-726
16. Fan Y. Testing the goodness of fit of a parametric density function by kernel method. Econom. Theory 10 (1994) 316-356
17. Fan Y. Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters. Econom. Theory 14 (1998) 604-621
18. Fang H.-B., Fang K.-T., and Kotz S. The meta-elliptical distributions with given marginals. J. Multivariate Anal. 82 (2002) 1-16
19. Farrel P.J., Salibian-Barrera M., and Naczk K. On tests for multivariate normality and associated simulation studies. J. Stat. Comput. Simul. 77 (2007) 1065-1080
20. Gouriéroux C., and Tenreiro C. Local power properties of kernel based goodness of fit tests. J. Multivariate Anal. 78 (2001) 161-190
21. Gregory G.G. On efficiency and optimality of quadratic tests. Ann. Statist. 8 (1980) 116-131
22. Hall P. The Bootstrap and Edgeworth Expansion (1997), Springer, New York
23. Henze N., and Zirkler B. A class of invariant consistent tests for multivariate normality. Comm. Stat. Theory Methods 19 (1990) 3595-3617
24. Henze N. Extreme smoothing and testing for multivariate normality. Statist. Probab. Lett. 35 (1997) 203-213
25. Henze N., and Wagner T. A new approach to the BHEP tests for multivariate normality. J. Multivariate Anal. 62 (1997) 1-23
26. Johnson M.E., Tietjen G.L., and Beckman R.J. A new family of probability distributions with applications to Monte Carlo studies. J. Amer. Statist. Assoc. 75 (1980) 276-279
27. Johnson M.E. Multivariate Statistical Simulation (1987), Wiley, New York
28. Mecklin C.J., and Mundfrom D.J. A Monte Carlo comparison of type I and type II error rates of tests of multivariate normality. J. Stat. Comput. Simul. 75 (2005) 93-107
29. Nikitin Y. Asymptotic Efficiency of Nonparametric Tests (1995), Cambridge University Press
30. R Development Core Team. R: A Language and Environment for Statistical Computing (2006), R Foundation for Statistical Computing, Vienna, Austria
31. Ramberg J.S., and Schmeiser B.W. An approximate method for generating asymmetric random variables. Commun. ACM 17 (1974) 78-82
32. Romeu J.L., and Ozturk A. A comparative study of goodness-of-fit tests for multivariate normality. J. Multivariate Anal. 46 (1993) 309-334
33. Tenreiro C. On the role played by the fixed bandwidth in the Bickel-Rosenblatt goodness-of-fit test. SORT 29 (2005) 201-216
34. Tenreiro C. On the asymptotic behaviour of location-scale invariant Bickel-Rosenblatt tests. J. Statist. Plann. Inference 137 (2007) 103-116
35. Yazici B., and Yolacan S. A comparison of various tests of normality. J. Stat. Comput. Simul. 77 (2007) 175-183