Volume 9, June 2005
|Page(s)||1 - 18|
|Published online||15 November 2005|
- P. Bickel and Y. Ritov, Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhya Ser. A. 50 (1989) 381–393.
- L. Birgé and P. Massart, Estimation of integral functionals of a density. Ann. Statist. 23 (1995) 11–29. [CrossRef] [MathSciNet]
- L. Birgé and P. Massart, Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 (1998) 329–375. [CrossRef] [MathSciNet]
- L. Birgé and Y. Rozenholc, How many bins should be put in a regular histogram. Technical Report Université Paris 6 et 7 (2002).
- J. Bretagnolle, A new large deviation inequality for U-statistics of order 2. ESAIM: PS 3 (1999) 151–162. [CrossRef] [EDP Sciences]
- D. Donoho and M. Nussbaum, Minimax quadratic estimation of a quadratic functional. J. Complexity 6 (1990) 290–323. [CrossRef] [MathSciNet]
- S. Efroïmovich and M. Low, On Bickel and Ritov's conjecture about adaptive estimation of the integral of the square of density derivatives. Ann. Statist. 24 (1996) 682–686. [CrossRef] [MathSciNet]
- S. Efroïmovich and M. Low, On optimal adaptive estimation of a quadratic functional. Ann. Statist. 24 (1996) 1106–1125. [CrossRef] [MathSciNet]
- M. Fromont and B. Laurent, Adaptive goodness-of-fit tests in a density model. Technical report. Université Paris 11 (2003).
- G. Gayraud and K. Tribouley, Wavelet methods to estimate an integrated quadratic functional: Adaptivity and asymptotic law. Statist. Probab. Lett. 44 (1999) 109–122. [CrossRef] [MathSciNet]
- E. Giné, R. Latala and J. Zinn, Exponential and moment inequalities for U-statistics. High Dimensional Probability 2, Progress in Probability 47 (2000) 13–38.
- W. Hardle, G. Kerkyacharian, D. Picard, A. Tsybakov, Wavelets, Approximations and statistical applications. Lect. Notes Stat. 129 (1998).
- C. Houdré and P. Reynaud-Bouret, Exponential inequalities for U-statistics of order two with constants, in Euroconference on Stochastic inequalities and applications. Barcelona. Birkhauser (2002).
- I.A. Ibragimov, A. Nemirovski and R.Z. Hasminskii, Some problems on nonparametric estimation in Gaussian white noise. Theory Probab. Appl. 31 (1986) 391–406. [CrossRef]
- I. Johnstone, Chi-square oracle inequalities. State of the art in probability and statistics (Leiden 1999) - IMS Lecture Notes Monogr. Ser., 36. Inst. Math. Statist., Beachwood, OH (1999) 399–418.
- B. Laurent, Efficient estimation of integral functionals of a density. Ann. Statist. 24 (1996) 659–681. [CrossRef] [MathSciNet]
- B. Laurent, Estimation of integral functionals of a density and its derivatives. Bernoulli 3 (1997) 181–211.
- B. Laurent and P. Massart, Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 (2000) 1302–1338. [CrossRef] [MathSciNet]
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