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Probability Theory and Related Fields

Volumn 71, Issue 2, 1986, Pages 271-291

On estimating a density using Hellinger distance and some other strange facts

(1) Birgé, Lucien a,b

a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE (France)

b MATHEMATICAL SCIENCES RESEARCH INSTITUTE (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000864703 PISSN: 01788051 EISSN: 14322064 Source Type: Journal
DOI: 10.1007/BF00332312 Document Type: Article

Times cited : (78)

References (19)

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- Birgé, L.: Thèse, 3^e-partie. Université Paris VII (1980)

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- Approximation dans les espaces métriques et théorie de l'estimation
- (1983) Z. Wahrscheinlichkeitstheor. Verw. Geb. , vol.65 , pp. 181-237
- Birgés, L.¹

4
- 84935793414
- Birgé, L.: Non-asymptotic minimax risk for Hellinger balls. Probability and Math. Statistics. To appear

5
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- Estimation des densités: risque minimax
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6
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- Lecture Notes in Mathematics, no 678, Springer, Berlin-Heidelberg-New York
- (1977) École d'Eté de Probabilités de Saint-Flour VII
- Dacunha-Castelle, D.¹

7
- 0001753901
- On arbitrarily slow rates of convergence in density estimation
- (1983) Z. Wahrscheinlichkeitstheor. Verw. Gebiete , vol.62 , pp. 475-483
- Devroye, L.¹

8
- 0039666461
- Estimation of distribution density
- (1980) Zap. Nauchn. Semin. LOMI , vol.98 , pp. 61-85
- Ibragimov, I.A.¹ Khas'minskii, R.Z.²

9
- 0039666462
- On the non-parametric density function
- (1981) Zap. Nauchn. Semin. LOMI , vol.108 , pp. 73-89
- Ibragimov, I.A.¹ Khas'minskii, R.Z.²

10
- 0003789496
- Springer, Berlin-Heidelberg-New York
- (1981) Statistical Estimation, Asymptotic Theory
- Ibragimov, I.A.¹ Khas'minskii, R.Z.²

11
- 0009387419
- A lower bound on the risks of non-parametric estimates of densities in the uniform metric
- (1978) Theory Probab. Appl. , vol.23 , pp. 794-796
- Khas'minskii, R.Z.¹

12
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- ε-entropy and ε-capacity of sets in function spaces
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- Kolmogorov, A.N.¹ Tikhomirov, V.M.²

13
- 0001786903
- Convergence of estimates under dimensionality restrictions
- (1973) The Annals of Statistics , vol.1 , pp. 38-53
- Le Cam, L.¹

14
- 84935824727
- LeCam, L.: Asymptotic methods in statistical decision theory. To be published

15
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- Metric entropy and approximation
- (1966) Bulletin of the American Mathematical Society , vol.72 , pp. 903-937
- Lorentz, G.G.¹

16
- 0004162546
- Holt, Rinehart, Winston, New York
- (1966) Approximation of Functions
- Lorentz, G.G.¹

17
- 0009114930
- Optimal convergence properties of kernel estimates of derivatives of a density function
- T., Gasser, M., Rosenblatt, Lecture Notes in Mathematics, no. 757, Springer, Berlin-Heidelberg-New York
- (1979) Smoothing Techniques for Curve Estimation , pp. 144-154
- Müller, H.G.¹ Gasser, T.²

18
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- Optimal rates of convergence for nonparametric estimators
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19
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- Stone, C.J.: Optimal uniform rate of convergence for nonparametric estimators of a density function or its derivatives. University of California Berkeley: preprint (1983)

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