Goodness-of-fit tests based on the kernel density estimator

Scandinavian Journal of Statistics

Volumn 32, Issue 4, 2005, Pages 599-616

  Cao, Ricardo ^a   Lugosi, Gábor ^b  

^a UNIVERSITY OF A CORUÑA   (Spain)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Bandwidth; Goodness of fit test; Kernel density estimator; Smoothing factor selection

Indexed keywords

EID: 28044456714     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2005.00471.x     Document Type: Article

References (23)

1. Ahmad, I. A. & Cerrito, P. B. (1993). Goodness of fit tests based on the L2-norm of multivariate probability density functions. J. Nonparametr. Statist. 2, 169-181.
2. Akaike, H. (1954). An approximation to the density function. Ann. Inst. Statist. Math. 6, 127-132.
3. Bickel, P. J. & Rosenblatt, M. (1973). On some global measures of the deviation of density function estimates. Ann. Statist. 1, 1071-1095.
4. Devroye, L. (1987). A course in density estimation. Birkhäuser, Boston.
5. Devroye, L. (1991). Exponential inequalities in nonparametric estimation. In Nonparametric functional estimation and related topics (ed. G. Roussas), 31-44. NATO ASI Series, Kluwer Academic Publishers, Dordrecht.
6. 1 view. John Wiley, New York.
7. Devroye, L. & Lugosi, G. (2000). Combinatorial methods in density estimation. Springer-Verlag, New York.
8. Devroye, L. & Lugosi, G. (2002). Almost sure classification of densities. J. Nonparametr. Statist. 14, 675-698.
9. Eggermont, P. P. B. & LaRiccia, V. N. (2001). Maximum penalized likelihood estimation, volume I: Density estimation. Springer-Verlag, New York.
10. Fan, Y. (1994). Testing the goodness of fit of a parametric density function by kernel method. Econ. Theory 10, 316-356.
11. Fan, Y. (1998). Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters. Econ. Theory 14, 604-621.
12. Györfi, L. & van der Meulen, E. C. (1991). A consistent goodness of fit test based on the total variation distance. In Nonparametric functional estimation and related topics (ed. G. Roussas), 631-646. NATO ASI Series, Kluwer Academic Publishers. Dordrecht.
13. Härdle, W. & Kneip, A. (1999). Testing a regression model when we have smooth alternatives in mind. Scand. J. Statist. 26, 221-238.
14. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13-30.
15. Hoeffding, W. & Wolfowitz, J. (1958). Distinguishability of sets of distributions. Ann. Math. Statist. 29, 700-718.
16. Kolmogorov, A. N. & Tikhomirov, V. M. (1961). ε-entropy and ε-capacity of sets in function spaces. Translat. Am. Math. Soc. 17, 277-364.
17. LeCam, L. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 1, 38-53.
18. Lepski, O. V. & Tsybakov, A. B. (2000). Asymptotically exact nonparametric hypothesis testing in supnorm and at a fixed point. Probab. Theory Related Fields 117, 17-48.
19. Marron, J. S. & Wand, M. P. (1992). Exact mean integrated square error. Ann. Statist. 20, 712-736.
20. McDiarmid, C. (1989). On the method of bounded differences. In Surveys in combinatorics 1989 (ed. J. Siemens), 148-188. Cambridge University Press, Cambridge.
21. Parzen, E. (1962). On the estimation of a probability density function and the mode. Ann. Math. Statist. 33, 1065-1076.
22. Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27, 832-837.
23. Rosenblatt, M. (1975). A quadratic measure of deviation of two-dimensional density estimates and a test of independence. Ann. Statist. 3, 1-14.