Almost sure classification of densities

Journal of Nonparametric Statistics

Volumn 14, Issue 6, 2002, Pages 675-698

  Devroye, Luc ^a   Lugosi, Gábor ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Asymptotic optimality; Convergence; Density estimation; Discernibility; Hypothesis testing; Kernel estimate; Minimax rate; Minimum distance estimation; Total boundedness

Indexed keywords

EID: 0036905364     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250215323     Document Type: Article

References (28)

1. Cover, T.M. (1973). On determining the irrationality of the mean of a random variable. Annals of Statistics, 1, 862.
2. Dembo, A. and Peres, Y. (1994). A topological criterion for hypothesis testing. Annals of Statistics, 22, 106-117.
3. Devroye, L. (1983). On arbitrarily slow rates of global convergence in density estimation. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 62, 475-483.
4. Devroye, L. (1984). A simple algorithm for generating random variates with a log-concave density. Computing, 33, 247-257.
5. Devroye, L. (1985). A note on the L1 consistency of variable kernel estimates. Annals of Statistics, 13, 1041-1049.
6. Devroye, L. (1987). A Course in Density Estimation. Birkhäuser Verlag, Boston.
7. Devroye, L. (1988). Asymptotic performance bounds for the kernel estimate. Annals of Statistics, 16, 1162-1179.
8. Devroye, L. (1989). Nonparametric density estimates with improved performance on given sets of densities. Statistics (Mathematische Operationsforschung und Statistik), 20, 357-376.
9. Devroye, L. and Györfi, L. (1985). Nonparametric Density Estimation: The L1 View. John Wiley, New York.
10. Devroye, L., Györfi, L. and Lugosi, G. (1996). A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York.
11. Devroye, L. and Lugosi, G. (1996). A universally acceptable smoothing factor for kernel density estimation. Annals of Statistics, 24, 2499-2512.
12. Devroye, L. and Lugosi, G. (1997). Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes. Annals of Statistics, 25, 2626-2637.
13. Devroye, L., Lugosi, G. and Udina, F. (2000). Inequalities for a new data-based method for selecting nonparametric densitys. In: Puff, M.L. (Ed.), Festschrift in Honour of George Roussas, VSP International Science Publishers.
14. Donoho, D.L. (1988). One-sided inference about functionals of a density. Annals of Statistics, 16, 1390-1420.
15. Fanin, G. (1993). Curves and Surfaces for Computer Aided Geometric Design, 3rd ed. Academic Press, Boston.
16. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58, 13-30.
17. Hoeffding, W. and Wolfowitz, J. (1958). Distinguishability of sets of distributions. Annals of Mathematical Statistics, 29, 700-718.
18. Koplowitz, J. (1977). Abstracts of papers. In: International Symposium on Information Theory, Cornell University, Ithaca, NY, p. 64.
19. Kulkarni, S.R. and Zeitouni, O. (1995). A general classification rule for probability measures. Annals of Statistics, 23, 1393-1407.
20. LeCam, L. and Schwartz, L. (1960). A necessary and sufficient condition for the existence of consistent estimates. Annals of Mathematical Statistics, 31, 140-150.
21. Lorentz, G.G. (1966). Approximation of Functions. Holt, Rinehart and Winston, New York.
22. Massart, P. (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Annals of Probability, 18, 1269-1283.
23. McDiarmid, C. (1989). On the method of bounded differences. In: Siemons, J. (Ed.), Surveys in Combinatorics, Vol. 141, London Mathematical Society Lecture Note Series. Cambridge University Press, pp. 148-188.
24. Royden, H.L. (1968). Real Analysis. Macmillan Publishing Co., New York.
25. Vapnik, V.N. and Chervonenkis, A. Ya. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications, 16, 264-280.
26. Wheeden, R.L. and Zygmund, A. (1977). Measure and Integral. Marcel Dekker, New York.
27. Yatracos, Y.G. (1985). Rates of convergence of minimum distance estimators and Kolmogorov's entropy. Annals of Statistics, 13, 768-774.
28. 1 consistent estimation. Canadian Journal of Statistics, 16, 283-292.