The LIL for the Bickel-Rosenblatt test statistic

Journal of Statistical Planning and Inference

Volumn 137, Issue 6, 2007, Pages 1829-1837

  Liang, Han Ying ^a   Jing, Bing Yi ^b  

^a TONGJI UNIVERSITY   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Bickel Rosenblatt test statistic; Fixed alternative; Kernel density estimator; Law of the iterated logarithm

Indexed keywords

EID: 33846389403     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2006.06.036     Document Type: Article

References (20)

1. d'Agostino R.B., and Stephens M.A. Goodness-of-fit Techniques (1986), Marcel Dekker Inc., New York
2. Bachmann, D., Dette, H., 2004. A note on the Bickel-Rosenblatt test in autoregressive time. Manuscript.
3. Berger J.O., and Delampady M. Testing precise hypotheses. With comments and a rejoinder by the authors. Statist. Sci. 2 3 (1987) 317-352
4. Bickel P.J., and Rosenblatt M. On some global measures of the deviations of density function estimates. Ann. Statist 1 (1973) 1071-1095
5. Chebana F. On the optimization of the weighted Bickel-Rosenblatt test. Statist. Probab. Lett. 68 (2004) 333-345
6. 2-deviation of the kernel density estimation indexed by classes of weight functions. J. Statist. Plann. Inference, 136, 2470-2505.
7. p-norms of density estimators. Probab. Theory and Related Fields 80 (1988) 269-291
8. p distances of kernel estimators of densities under random censorship. Ann. Statist 19 (1991) 1813-1831
9. De la Peña, and Giné E. Decoupling: From Dependence to Independence (1999), Springer, New York
10. Giné E., and Mason D. The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator. Bernoulli 10 4 (2004) 721-752
11. 1-norm density estimator process. Ann. Probab. 31 2 (2003) 719-768
12. Hall P. Central limit theorem for integrated square error of multivariate nonparametric density estimators. J. Multivar. Anal. 14 (1984) 1-16
13. p-norms of multivariate density estimators. Ann. Statist. 19 (1991) 1933-1949
14. Lee S., and Na S. On the Bickel-Rosenblatt test for first-order autoregressive models. Statist. Probab. Lett. 65 1 (2002) 23-35
15. Lehmann E.L. Testing Statistical Hypotheses (1986), Wiley, New York
16. 2-type statistics in density testing. Statist. Probab. Lett. 50 2 (2000) 137-147
17. Sellke T., Bayarri M.J., and Berger J.O. Calibration of p values for testing precise null hypotheses. Amer. Statist. 55 1 (2001) 62-71
18. Stein E.M. Singular Integrals and Differentiability Properties of Functions (1970), Princeton University Press, Princeton, NJ
19. Takahata H., and Yoshihara K.I. Central limit theorems for integrated square error of nonparametric density estimators based on absolutely regular random sequences. Yokohama Math. J. 35 1/2 (1987) 95-111
20. Tenreiro, C., 2006. On the asymptotic behaviour of location-scale invariant Bickel-Rosenblatt tests. J. Statist. Plann. Inference, in press, doi: 10.1016/j.jspi.2005.11.006.