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Volumn 38, Issue 2, 2010, Pages 1122-1170

Confidence bands in density estimation

Author keywords

Adaptive estimation; Density estimation; Extremes; Gaussian processes; Kernel estimators; Limit theorem; Wavelet estimators

Indexed keywords


EID: 77649285528     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS738     Document Type: Article
Times cited : (163)

References (44)
  • 1
    • 0001236183 scopus 로고
    • Über die Baire'sche Kategorie gewisser Funktionenmengen
    • BANACH, S. (1931). Über die Baire'sche Kategorie gewisser Funktionenmengen. Studia Math. 3 174-179.
    • (1931) Studia Math. , vol.3 , pp. 174-179
    • Banach, S.1
  • 2
    • 24344434625 scopus 로고    scopus 로고
    • Confidence balls in Gaussian regression
    • BARAUD, Y. (2004). Confidence balls in Gaussian regression. Ann. Statist. 32 528-551.
    • (2004) Ann. Statist. , vol.32 , pp. 528-551
    • Baraud, Y.1
  • 3
    • 0039394747 scopus 로고    scopus 로고
    • Modulation of estimators and confidence sets
    • BERAN, R. and DÜMBGEN, L. (1998). Modulation of estimators and confidence sets. Ann. Statist. 26 1826-1856.
    • (1998) Ann. Statist. , vol.26 , pp. 1826-1856
    • Beran, R.1    Dümbgen, L.2
  • 4
    • 0000797991 scopus 로고
    • On some global measures of the deviations of density function estimates
    • Correction (1975) 3 1370
    • BICKEL, P. and ROSENBLATT, M. (1973). On some global measures of the deviations of density function estimates. Ann. Statist. 1 1071-1095. Correction (1975) 3 1370.
    • (1973) Ann. Statist. , vol.1 , pp. 1071-1095
    • Bickel, P.1    Rosenblatt, M.2
  • 5
    • 24344508204 scopus 로고    scopus 로고
    • An adaptation theory for nonparametric confidence intervals
    • CAI, T. T. and LOW, M. G. (2004). An adaptation theory for nonparametric confidence intervals. Ann. Statist. 32 1805-1840.
    • (2004) Ann. Statist. , vol.32 , pp. 1805-1840
    • Cai, T.T.1    Low, M.G.2
  • 6
    • 33644903538 scopus 로고    scopus 로고
    • Adaptive confidence balls
    • CAI, T. T. and LOW, M. G. (2006). Adaptive confidence balls. Ann. Statist. 34 202-228.
    • (2006) Ann. Statist. , vol.34 , pp. 202-228
    • Cai, T.T.1    Low, M.G.2
  • 8
    • 69049098949 scopus 로고    scopus 로고
    • Nonparametric regression, confidence regions and regularization
    • DAVIES, P. L., KOVAC, A. and MEISE, M. (2009). Nonparametric regression, confidence regions and regularization. Ann. Statist. 37 2597-2625.
    • (2009) Ann. Statist. , vol.37 , pp. 2597-2625
    • Davies, P.L.1    Kovac, A.2    Meise, M.3
  • 9
    • 0001036557 scopus 로고
    • Maxima and minima of stationary sequences
    • DAVIS, R. A. (1979). Maxima and minima of stationary sequences. Ann. Probab. 7 453-460.
    • (1979) Ann. Probab. , vol.7 , pp. 453-460
    • Davis, R.A.1
  • 11
    • 0001151383 scopus 로고
    • An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions
    • Springer, Berlin
    • DUDLEY, R. M. (1985). An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions. In Probability in Banach Spaces, V (Medford, MA, 1984). Lecture Notes in Math. 1153 141-178. Springer, Berlin.
    • (1985) Probability in Banach Spaces, v (Medford, MA, 1984). Lecture Notes in Math. , Issue.1153 , pp. 141-178
    • Dudley, R.M.1
  • 13
    • 3042530624 scopus 로고    scopus 로고
    • Optimal confidence bands for shape-restricted curves
    • DÜMBGEN, L. (2003). Optimal confidence bands for shape-restricted curves. Bernoulli 9 423-449.
    • (2003) Bernoulli , vol.9 , pp. 423-449
    • Dümbgen, L.1
  • 14
    • 22944431500 scopus 로고    scopus 로고
    • Nonparametric confidence sets for wavelet regression
    • GENOVESE, C. and WASSERMAN, L. (2005). Nonparametric confidence sets for wavelet regression. Ann. Statist. 33 698-729
    • (2005) Ann. Statist. , vol.33 , pp. 698-729
    • Genovese, C.1    Wasserman, L.2
  • 15
    • 51049112271 scopus 로고    scopus 로고
    • Adaptive confidence bands
    • GENOVESE, C. and WASSERMAN, L. (2008). Adaptive confidence bands. Ann. Statist. 36 875-905
    • (2008) Ann. Statist. , vol.36 , pp. 875-905
    • Genovese, C.1    Wasserman, L.2
  • 16
    • 0036847557 scopus 로고    scopus 로고
    • Rates of strong uniform consistency for multivariate kernel density estimators
    • GINÉ, E. and GUILLOU, A. (2002). Rates of strong uniform consistency for multivariate kernel density estimators. Ann. Inst. H. Poincaré Probab. Statist. 38 907-921.
    • (2002) Ann. Inst. H. Poincaré Probab. Statist. , vol.38 , pp. 907-921
    • Giné, E.1    Guillou, A.2
  • 17
    • 5644227769 scopus 로고    scopus 로고
    • Kernel density estimators: Convergence in distribution for weighted sup-norms
    • DOI 10.1007/s00440-004-0339-x
    • GINÉ, E., KOLTCHINSKII, V. and SAKHANENKO, L. (2004). Kernel density estimators: Convergence in distribution for weighted sup-norms. Probab. Theory Related Fields 130 167-198. (Pubitemid 39374503)
    • (2004) Probability Theory and Related Fields , vol.130 , Issue.2 , pp. 167-198
    • Gine, E.1    Koltchinskii, V.2    Sakhanenko, L.3
  • 19
    • 77649293894 scopus 로고    scopus 로고
    • Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections
    • To appear
    • GINÉ, E. and NICKL, R. (2010). Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections. Bernoulli. To appear.
    • (2010) Bernoulli
    • Giné, E.1    Nickl, R.2
  • 20
    • 59449098498 scopus 로고    scopus 로고
    • An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation
    • GINÉ, E. and NICKL, R. (2009a). An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation. Probab. Theory Related Fields 143 569-596.
    • (2009) Probab. Theory Related Fields , vol.143 , pp. 569-596
    • Giné, E.1    Nickl, R.2
  • 21
    • 69849086811 scopus 로고    scopus 로고
    • Uniform limit theorems for wavelet density estimators
    • GINÉ, E. and NICKL, R. (2009b). Uniform limit theorems for wavelet density estimators. Ann. Probab. 37 1605-1646.
    • (2009) Ann. Probab. , vol.37 , pp. 1605-1646
    • Giné, E.1    Nickl, R.2
  • 22
    • 54349118425 scopus 로고    scopus 로고
    • Structural adaptation via Lp-norm oracle inequalities
    • GOLDENSHLUGER, A. and LEPSKI, O. (2009). Structural adaptation via Lp-norm oracle inequalities. Probab. Theory Related Fields 143 41-71.
    • (2009) Probab. Theory Related Fields , vol.143 , pp. 41-71
    • Goldenshluger, A.1    Lepski, O.2
  • 23
    • 0001260350 scopus 로고
    • Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density
    • HALL, P. (1992). Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density. Ann. Statist. 20 675-694.
    • (1992) Ann. Statist. , vol.20 , pp. 675-694
    • Hall, P.1
  • 25
    • 21844522284 scopus 로고
    • Finite-sample confidence envelopes for shaperestricted densities
    • HENGARTNER, N. W. and STARK, P. B. (1995). Finite-sample confidence envelopes for shaperestricted densities. Ann. Statist. 23 525-550.
    • (1995) Ann. Statist. , vol.23 , pp. 525-550
    • Hengartner, N.W.1    Stark, P.B.2
  • 26
    • 0036278271 scopus 로고    scopus 로고
    • Random rates in anisotropic regression
    • HOFFMANN, M. and LEPSKI, O. (2002). Random rates in anisotropic regression (with discussion). Ann. Statist. 30 325-396.
    • (2002) Ann. Statist. , vol.30 , pp. 325-396
    • Hoffmann, M.1    Lepski, O.2
  • 27
    • 0043223519 scopus 로고    scopus 로고
    • Extremes of Gaussian processes, on results of Piterbarg and Seleznjev
    • HÜSLER, J. (1999). Extremes of Gaussian processes, on results of Piterbarg and Seleznjev. Statist. Probab. Lett. 44 251-258.
    • (1999) Statist. Probab. Lett. , vol.44 , pp. 251-258
    • Hüsler, J.1
  • 28
    • 0348173778 scopus 로고    scopus 로고
    • On convergence of the uniform norms for Gaussian processes and linear approximation problems
    • HÜSLER, J., PITERBARG, V. and SELEZNJEV, O. (2003). On convergence of the uniform norms for Gaussian processes and linear approximation problems. Ann. Appl. Probab. 13 1615-1653.
    • (2003) Ann. Appl. Probab. , vol.13 , pp. 1615-1653
    • Hüsler, J.1    Piterbarg, V.2    Seleznjev, O.3
  • 29
    • 0031515850 scopus 로고    scopus 로고
    • Multifractal formalism for functions. I. Results valid for all functions
    • JAFFARD, S. (1997). Multifractal formalism for functions. I. Results valid for all functions. SIAM J. Math. Anal. 28 944-970.
    • (1997) SIAM J. Math. Anal. , Issue.28 , pp. 944-970
    • Jaffard, S.1
  • 30
    • 0034195869 scopus 로고    scopus 로고
    • On the Frisch-Parisi conjecture
    • JAFFARD, S. (2000). On the Frisch-Parisi conjecture. J. Math. Pures Appl. 79 525-552.
    • (2000) J. Math. Pures Appl. , vol.79 , pp. 525-552
    • Jaffard, S.1
  • 32
    • 0000411204 scopus 로고
    • An approximation of partial sums of independent rv's, and the sample df. I.
    • KOMLÓS, J.,MAJOR, J. and TUSNÁDY, G. (1975). An approximation of partial sums of independent rv's, and the sample df. I. Z. Wahrsch. Verw. Gebiete 32 111-131.
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 111-131
    • Komlós, J.1    Major, J.2    Tusnády, G.3
  • 33
    • 21144472140 scopus 로고
    • Extreme values of the cyclostationary Gaussian random processes
    • KONSTANT, D. G. and PITERBARG, V. I. (1993). Extreme values of the cyclostationary Gaussian random processes. J. Appl. Probab. 30 82-97.
    • (1993) J. Appl. Probab. , vol.30 , pp. 82-97
    • Konstant, D.G.1    Piterbarg, V.I.2
  • 35
    • 0040276000 scopus 로고
    • Honest confidence regions for nonparametric regression
    • LI, K. C. (1989). Honest confidence regions for nonparametric regression. Ann. Statist. 17 1001-1008.
    • (1989) Ann. Statist. , vol.17 , pp. 1001-1008
    • Li, K.C.1
  • 36
    • 0031327278 scopus 로고    scopus 로고
    • On nonparametric confidence intervals
    • LOW, M. G. (1997). On nonparametric confidence intervals. Ann. Statist. 25 2547-2554.
    • (1997) Ann. Statist. , vol.25 , pp. 2547-2554
    • Low, M.G.1
  • 38
    • 0000579826 scopus 로고
    • U-processes: Rates of convergence
    • NOLAN, D. and POLLARD, D. (1987). U-processes: Rates of convergence. Ann. Statist. 15 780-799.
    • (1987) Ann. Statist. , vol.15 , pp. 780-799
    • Nolan, D.1    Pollard, D.2
  • 39
    • 0034375491 scopus 로고    scopus 로고
    • Adaptive confidence interval for pointwise curve estimation
    • PICARD, D. and TRIBOULEY, K. (2000). Adaptive confidence interval for pointwise curve estimation. Ann. Statist. 28 298-335.
    • (2000) Ann. Statist. , vol.28 , pp. 298-335
    • Picard, D.1    Tribouley, K.2
  • 41
    • 33744826821 scopus 로고    scopus 로고
    • Adaptive nonparametric confidence sets
    • ROBINS, J. and VAN DER VAART, A. W. (2006). Adaptive nonparametric confidence sets. Ann. Statist. 34 229-253.
    • (2006) Ann. Statist. , vol.34 , pp. 229-253
    • Robins, J.1    Van Der Vaart, A.W.2
  • 42
    • 0004016842 scopus 로고
    • Krieger, Malabar. (Correlated reprint of the 1981 original.)
    • SCHUMAKER, L. L. (1993). Spline Functions: Basic Theory. Krieger, Malabar. (Correlated reprint of the 1981 original.)
    • (1993) Spline Functions: Basic Theory.
    • Schumaker, L.L.1
  • 43
    • 0042431681 scopus 로고
    • On the construction of confidence regions for the density of distribution of random variables
    • Russian
    • SMIRNOV, N. V. (1950). On the construction of confidence regions for the density of distribution of random variables. Doklady Akad. Nauk SSSR 74 189-191 (Russian).
    • (1950) Doklady Akad. Nauk SSSR , vol.74 , pp. 189-191
    • Smirnov, N.V.1
  • 44
    • 0030489977 scopus 로고    scopus 로고
    • New concentration inequalities in product spaces
    • TALAGRAND, M. (1996). New concentration inequalities in product spaces. Invent. Math. 126 505-563. (Pubitemid 126323770)
    • (1996) Inventiones Mathematicae , vol.126 , Issue.3 , pp. 505-563
    • Talagrand, M.1


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