Nonparametric testing the similarity of two unknown density functions: Local power and bootstrap analysis

Journal of Nonparametric Statistics

Volumn 11, Issue 1-3, 1999, Pages 189-213

  Li, Qi ^a,b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF GUELPH   (Canada)

Author keywords

Boot strap method; Kernel estimation; Nonparametric test; Singular local alternative; Smoothing parameter; Unknown densities

Indexed keywords

EID: 0347140940     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259908832780     Document Type: Article

References (18)

1. Ahmad, I. A. (1980) "Nonparametric estimation of an affinity measure between two absolutely continuous distributions with hypothesis testing applications", Ann. Inst. Stat. Math. Part A, 32, 223-240.
2. Ahmad, I. A. and Van Belle, G. (1974) "Measuring affinity of distributions", Reliability and Biometry, Statistical Analysis of Life Testing (Eds. Proschan and Serfling, R. J.). SIAM, Philadelphia, pp. 651-668.
3. Anderson, N. H., Hall, P. and Titterington, D. M. (1994) "Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates", Journal of Multivariate Analysis, 50, 41-54.
4. Barndorff-Nielsen, O. E. and Cox, D. R. (1989) Asymptotic Techniques for Use in Statistics. London: Chapman and Hall.
5. Bickel, P. J., Götze, F. and van Zwet, W. R. (1986) "The Edgeworth expansion for U-statistics of degree two", Annals of Statistics, 14, 1463-1484.
6. Bickel, P. J. and Rosenblatt, M. (1971) "On some global measures of the derivations of density function estimates". Annals of Statistics, 1, 1071-1095.
7. Fan, Y. (1994) "Testing goodness-of-fit of a parametric density function by kernel method", Econometric Theory, 10, 316-356.
8. Fan, Y. and Gencay, R. (1993) "Hypotheses testing based on modified nonparametric estimation of an affinity measure between two distributions", Journal of Nonparametric Statistics, 4, 389-403.
9. Fan, Y. and Li, Q. (1996) "Consistent model specification tests: Bierens' ICM tests versus kernel-based tests", technical report, University of Windsor.
10. Ghosh, B. K. and Wei-Min Huang (1991) "The power and optimal kernel of the Bickel-Rosenblatt test for goodness-of-fit", The Annals of Statistics, 19(2), 999-1009.
11. Hall, P. (1992) The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag.
12. Hall, P. (1984) "Central limit theorem for integrated square error of multivariate nonparametric density estimators", Annals of Statistics, 14, 1-16.
13. Helmers, R. (1991) "On the Edgeworth expansion and the bootstrap approximation for a studentized U-statistic", Annals of Statistics, 19, 470-484.
14. Li, Q. (1996) "Nonparametric testing of closeness between two unknown distribution functions", Econometric Reviews, 15, 261-274.
15. Li, Q. and Wang, S. (1994) "A simple consistent bootstrap test for parametric regression functional form", forthcoming in Journal of Econometrics.
16. Mammen, E. (1992) When does bootstrap work: Asymptotic results and Simulations. Lecture notes in Statistics. 77. Springer, Berlin.
17. Marron, J. S. and Wand, M. P. (1992) "Exact mean integrated square error", The Annals of Statistics, 20(2), 712-736.
18. Rosenblatt, M. A. (1975) "Quadratic measure of deviation of two-dimensional density estimates and a test of independence", Annals of Statistics, 3, 1-14.