On the role played by the fixed bandwidth in the Bickel-Rosenblatt goodness-of-fit test

SORT

Volumn 29, Issue 2, 2005, Pages 201-216

  Tenreiro, Carlos ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Bahadur efficiency; Goodness of fit test; Kernel density estimator

Indexed keywords

EID: 31944440201     PISSN: 16962281     EISSN: 20138830     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. and Sorensen, D. (1999). LAPACK users' guide, Third edition, SIAM, Philadelphia.
2. 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.
3. Bahadur, R.R. (1967). Rates of convergence of estimates and test statistics, Ann. Math. Statist., 38, 303-324.
4. Bahadur, R.R. (1971). Some Limit Theorems in Statistics, SIAM, Philadelphia.
5. Bickel, P.J., Rosenblatt, M. (1973). On some global measures of the deviations of density function estimates, Ann. Statist., 1, 1071-1095.
6. Bowman, A.W. (1992). Density based tests for goodness-of-fit normality, J. Statist. Comput. Simul., 40, 1-13.
7. Bowman, A.W., Foster, P.J. (1993). Adaptive smoothing and density-based tests of multivariate normality, J. Amer. Statist. Assoc., 88, 529-537.
8. Dunford, N., Schwartz, J.T. (1963). Linear Operators, Part II, Interscience Publishers, New York.
9. Durbin, J., Knott, M., Taylor, C.C. (1975). Components of Cramér-von Mises Statistics II, J. Roy. Statist. Soc. Ser. B, 37, 216-237.
10. Durio, A., Nikitin, Ya.Yu. (2003). Local Bahadur efficiency of some goodness-of-fit tests under skew alternatives, J. Statist. Plann. Inference, 115, 171-179. (Pubitemid 36535748)
11. Epps, T.W., Pulley, L.B. (1983). A test for normality based on the empirical characteristic function, Biometrika, 70, 723-726.
12. 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.
13. Fan, Y. (1994). Testing the goodness of fit of a parametric density function by kernel method, Econometric Theory, 10, 316-356.
14. Fan, Y. (1998). Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters, Econometric Theory, 14, 604-621.
15. Gouriéroux, C., Tenreiro, C. (2001). Local power properties of kernel based goodness of fit tests, J. Multivariate Anal., 78, 161-190. (Pubitemid 33377644)
16. Gregory, G.G. (1977). Large sample theory for U-statistics and tests of fit, Ann. Statist., 5, 110-123.
17. Gregory, G.G. (1980). On efficiency and optimality of quadratic tests, Ann. Statist., 8, 116-131.
18. Hall, P. (1997). The Bootstrap and Edgeworth Expansion, Springer, New York.
19. Henze, N., Zirkler, B. (1990). A class of invariante consistent tests for multivariate normality, Commun. Stat. Theory Methods, 19, 3595-3617.
20. Henze, N., Wagner, T. (1997). A new approach to the BHEP tests formultivariate normality, J. Multivariate Anal., 62, 1-23. (Pubitemid 127174725)
21. Koroljuk, V.S., Borovskich, Yu.V. (1989). Theory of U-Statistics, Kluwer, Dordrecht.
22. Nikitin, Y. (1995). Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press.
23. Parzen, E. (1962). On estimation of a probability density function and mode, Ann. Math. Statist., 33, 1065-1076.
24. Ramberg, J.S., Schmeiser, B.W. (1974). An approximate method for generating asymmetric random variables, Commun. ACM, 17, 78-82.
25. Rosenblatt, M. (1956). Remarks on some non-parametric estimates of a density function, Ann. Math. Statist., 27, 832-837.
26. Sethuraman, J. (1964). On the probability of large deviations of families of sample means, Ann. Math. Statist., 35, 1304-1316.
27. Stephens, M.A. (1986). Tests based on EDF statistics, In: Goodness-of-Fit Techniques, ed. D'Agostino, R.B. and Stephens, M.A., Marcel Dekker, New York, 97-193.