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Volumn 39, Issue 3, 2011, Pages 1608-1632

Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality

Author keywords

Adaptive estimation; Density estimation; Double struck Ls risk; Empirical process; Kernel estimators; Oracle inequalities

Indexed keywords


EID: 84858749056     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS883     Document Type: Article
Times cited : (219)

References (26)
  • 1
    • 77955146719 scopus 로고    scopus 로고
    • Available at arXiv:0808.1416v2
    • 2-loss. Available at arXiv:0808.1416v2.
    • (2008) 2-loss
    • Birgé, L.1
  • 2
    • 0000982196 scopus 로고
    • Estimation des densités: Risque minimax
    • MR0523165
    • BRETAGNOLLE, J. and HUBER, C. (1979). Estimation des densités: Risque minimax. Z. Wahrsch. Verw. Gebiete 47 119-137. MR0523165
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.47 , pp. 119-137
    • Bretagnolle, J.1    Huber, C.2
  • 4
    • 0030335054 scopus 로고    scopus 로고
    • A universally acceptable smoothing factor for kernel density estimates
    • MR1425963
    • DEVROYE, L. and LUGOSI, G. (1996). A universally acceptable smoothing factor for kernel density estimates. Ann. Statist. 24 2499-2512. MR1425963
    • (1996) Ann. Statist. , vol.24 , pp. 2499-2512
    • Devroye, L.1    Lugosi, G.2
  • 5
    • 0031319763 scopus 로고    scopus 로고
    • Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes
    • MR1604428
    • DEVROYE, L. and LUGOSI, G. (1997). Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes. Ann. Statist. 25 2626-2637. MR1604428
    • (1997) Ann. Statist. , vol.25 , pp. 2626-2637
    • Devroye, L.1    Lugosi, G.2
  • 8
    • 58149352562 scopus 로고    scopus 로고
    • Universal pointwise selection rule in multivariate function estimation
    • MR2543590
    • GOLDENSHLUGER, A. and LEPSKI, O. (2008). Universal pointwise selection rule in multivariate function estimation. Bernoulli 14 1150-1190. MR2543590
    • (2008) Bernoulli , vol.14 , pp. 1150-1190
    • Goldenshluger, A.1    Lepski, O.2
  • 10
    • 84861404590 scopus 로고    scopus 로고
    • Uniform bounds for norms of sums of independent random functions
    • To appear. Available at arXiv:0904.1950v2.
    • GOLDENSHLUGER, A. and LEPSKI, O. (2011). Uniform bounds for norms of sums of independent random functions. Ann. Probab. To appear. Available at arXiv:0904.1950v2.
    • (2011) Ann. Probab.
    • Goldenshluger, A.1    Lepski, O.2
  • 11
    • 0001253184 scopus 로고
    • On density estimation in the view of Kolmogorov's ideas in approximation theory
    • MR1062695
    • HASMINSKII, R. and IBRAGIMOV, I. (1990). On density estimation in the view of Kolmogorov's ideas in approximation theory. Ann. Statist. 18 999-1010. MR1062695
    • (1990) Ann. Statist. , vol.18 , pp. 999-1010
    • Hasminskii, R.1    Ibragimov, I.2
  • 14
    • 0000091003 scopus 로고
    • Asymptotic properties of non-linear least squares estimators
    • MR0238419
    • JENNRICH, R. I. (1969). Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40 633-643. MR0238419
    • (1969) Ann. Math. Statist. , vol.40 , pp. 633-643
    • Jennrich, R.I.1
  • 15
    • 0000537934 scopus 로고
    • Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
    • MR0770640
    • JOHNSON, W. B., SCHECHTMAN, G. and ZINN, J. (1985). Best constants in moment inequalities for linear combinations of independent and exchangeable random variables. Ann. Probab. 13 234-253. MR0770640
    • (1985) Ann. Probab. , vol.13 , pp. 234-253
    • Johnson, W.B.1    Schechtman, G.2    Zinn, J.3
  • 16
    • 33747354349 scopus 로고    scopus 로고
    • On minimax density estimation on ℝ
    • MR2046772
    • JUDITSKY, A. and LAMBERT-LACROIX, S. (2004). On minimax density estimation on ℝ. Bernoulli 10 187-220. MR2046772
    • (2004) Bernoulli , vol.10 , pp. 187-220
    • Juditsky, A.1    Lambert-Lacroix, S.2
  • 17
    • 0035643281 scopus 로고    scopus 로고
    • Nonlinear estimation in anisotropic multi-index denoising
    • MR1863916
    • KERKYACHARIAN, G., LEPSKI, O. and PICARD, D. (2001). Nonlinear estimation in anisotropic multi-index denoising. Probab. Theory Related Fields 121 137-170. MR1863916
    • (2001) Probab. Theory Related Fields , vol.121 , pp. 137-170
    • Kerkyacharian, G.1    Lepski, O.2    Picard, D.3
  • 20
    • 34247553430 scopus 로고    scopus 로고
    • Concentration Inequalities and Model Selection
    • Springer, Berlin. MR2319879
    • MASSART, P. (2007). Concentration Inequalities and Model Selection. Lecture Notes in Math. 1896. Springer, Berlin. MR2319879
    • (2007) Lecture Notes in Math. , vol.1896
    • Massart, P.1
  • 22
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • MR0143282
    • PARZEN, E. (1962). On estimation of a probability density function and mode. Ann. Math. Statist. 33 1065-1076. MR0143282
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 23
    • 77955137685 scopus 로고    scopus 로고
    • Linear and convex aggregation of density estimators
    • MR2356821
    • RIGOLLET, P. and TSYBAKOV, A. B. (2007). Linear and convex aggregation of density estimators. Math. Methods Statist. 16 260-280. MR2356821
    • (2007) Math. Methods Statist. , vol.16 , pp. 260-280
    • Rigollet, P.1    Tsybakov, A.B.2
  • 24
    • 0001529784 scopus 로고
    • Remarks on some nonparametric estimates of a density function
    • MR0079873
    • ROSENBLATT, M. (1956). Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 832-837. MR0079873
    • (1956) Ann. Math. Statist. , vol.27 , pp. 832-837
    • Rosenblatt, M.1
  • 25
    • 54349102452 scopus 로고    scopus 로고
    • Aggregation of density estimators and dimension reduction
    • In Advances in Statistical Modeling and Inference (V. Nair, ed.). World Scientific, Hackensack, NJ. MR2416118
    • SAMAROV, A. and TSYBAKOV, A. (2007). Aggregation of density estimators and dimension reduction. In Advances in Statistical Modeling and Inference (V. Nair, ed.). Ser. Biostat. 3 233-251. World Scientific, Hackensack, NJ. MR2416118
    • (2007) Ser. Biostat. , vol.3 , pp. 233-251
    • Samarov, A.1    Tsybakov, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.