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Volumn 34, Issue 1, 2006, Pages 229-253

Adaptive nonparametric confidence sets

Author keywords

Adaptation; Density estimation; Regression; Testing rate; White noise model

Indexed keywords


EID: 33744826821     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000877     Document Type: Article
Times cited : (79)

References (39)
  • 1
    • 24344434625 scopus 로고    scopus 로고
    • Confidence balls in Gaussian regression
    • MR2060168
    • BARAUD, Y. (2004). Confidence balls in Gaussian regression. Ann. Statist. 32 528-551. MR2060168
    • (2004) Ann. Statist. , vol.32 , pp. 528-551
    • Baraud, Y.1
  • 2
    • 0033459856 scopus 로고    scopus 로고
    • Risk bounds for model selection via penalization
    • MR1679028
    • BARRON, A., BIRGÉ, L. and MASSART, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301-413. MR1679028
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 301-413
    • Barron, A.1    Birgé, L.2    Massart, P.3
  • 3
    • 0026190366 scopus 로고
    • Minimum complexity density estimation
    • MR1111806
    • BARRON, A. R. and COVER, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37 1034-1054. MR1111806
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1034-1054
    • Barron, A.R.1    Cover, T.M.2
  • 4
    • 0442278086 scopus 로고    scopus 로고
    • REACT scatterplot smoothers: Superefficiency through basis economy
    • MR1803148
    • BERAN, R. (2000). REACT scatterplot smoothers: Superefficiency through basis economy. J. Amer. Statist. Assoc. 95 155-171, MR1803148
    • (2000) J. Amer. Statist. Assoc. , vol.95 , pp. 155-171
    • Beran, R.1
  • 5
    • 0039394747 scopus 로고    scopus 로고
    • Modulation of estimators and confidence sets
    • MR 1673280
    • BERAN, R. and DÜMBGEN, L. (1998). Modulation of estimators and confidence sets. Ann. Statist. 26 1826-1856. MR 1673280
    • (1998) Ann. Statist. , vol.26 , pp. 1826-1856
    • Beran, R.1    Dümbgen, L.2
  • 6
    • 0001667487 scopus 로고
    • Estimating integrated squared density derivatives: Sharp best order of convergence estimates
    • MR1065550
    • BlCKEL, P. J. and RITOV, Y. (1988). Estimating integrated squared density derivatives: Sharp best order of convergence estimates. Sankhyā Ser. A 50 381-393. MR1065550
    • (1988) Sankhyā Ser. A , vol.50 , pp. 381-393
    • Blckel, P.J.1    Ritov, Y.2
  • 7
    • 0043289755 scopus 로고    scopus 로고
    • Discussion of "Random rates in anisotropic regression"
    • by M. Hoffmann and O. Lepski, MR1902892
    • BIRGÉ, L. (2002). Discussion of "Random rates in anisotropic regression," by M. Hoffmann and O. Lepski. Ann. Statist. 30 359-363, MR1902892
    • (2002) Ann. Statist. , vol.30 , pp. 359-363
    • Birgé, L.1
  • 8
    • 0003281721 scopus 로고    scopus 로고
    • Gaussian model selection
    • MR1848946
    • BIRGÉ, L. and MASSART, P. (2001). Gaussian model selection. J. Eur. Math. Soc. 3 203-268. MR1848946
    • (2001) J. Eur. Math. Soc. , vol.3 , pp. 203-268
    • Birgé, L.1    Massart, P.2
  • 9
    • 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
  • 10
    • 21644472518 scopus 로고    scopus 로고
    • Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
    • MR2102503
    • BROWN, L. D., CARTER, A. V., LOW, M. G. and ZHANG, C.-H. (2004). Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. Ann. Statist. 32 2074-2097. MR2102503
    • (2004) Ann. Statist. , vol.32 , pp. 2074-2097
    • Brown, L.D.1    Carter, A.V.2    Low, M.G.3    Zhang, C.-H.4
  • 11
    • 33644903538 scopus 로고    scopus 로고
    • Adaptive confidence balls
    • CAI, T. and LOW, M. (2006). Adaptive confidence balls. Ann. Statist. 34 202-228.
    • (2006) Ann. Statist. , vol.34 , pp. 202-228
    • Cai, T.1    Low, M.2
  • 12
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinkage
    • MR1379464
    • DONOHO, D. L. and JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1200-1224
    • Donoho, D.L.1    Johnstone, I.M.2
  • 13
    • 0041958932 scopus 로고
    • Ideal spatial adaptation via wavelet shrinkage
    • MR1311089
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika 81 425-455. MR1311089
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 16
    • 84904776239 scopus 로고
    • Learning algorithm for nonparametric filtering
    • EFROMOVICH, S. YU. and PINSKER, M. S. (1984). Learning algorithm for nonparametric filtering. Autom. Remote Control 11 1434-1440.
    • (1984) Autom. Remote Control , vol.11 , pp. 1434-1440
    • Efromovich, S.Yu.1    Pinsker, M.S.2
  • 17
    • 0001097057 scopus 로고
    • On the estimation of quadratic functionals
    • MR1126325
    • FAN, J. (1991). On the estimation of quadratic functionals. Ann. Statist. 19 1273-1294. MR1126325
    • (1991) Ann. Statist. , vol.19 , pp. 1273-1294
    • Fan, J.1
  • 18
    • 22944431500 scopus 로고    scopus 로고
    • Confidence sets for nonparametric wavelet regression
    • MR2163157
    • GENOVESE, C. R. and WASSERMAN, L. (2005). Confidence sets for nonparametric wavelet regression. Ann. Statist. 33 698-729. MR2163157
    • (2005) Ann. Statist. , vol.33 , pp. 698-729
    • Genovese, C.R.1    Wasserman, L.2
  • 19
    • 0023207865 scopus 로고
    • Adaptive asymptotically minimax estimates of smooth signals
    • MR0893970
    • GOLUBEV, G. K. (1987). Adaptive asymptotically minimax estimates of smooth signals. Problems Inform. Transmission 23 57-67. MR0893970
    • (1987) Problems Inform. Transmission , vol.23 , pp. 57-67
    • Golubev, G.K.1
  • 20
    • 0036278271 scopus 로고    scopus 로고
    • Random rates in anisotropic regression (with discussion)
    • MR1902892
    • HOFFMANN, M. and LEPSKI, O. (2002). Random rates in anisotropic regression (with discussion). Ann. Statist. 30 325-396. MR1902892
    • (2002) Ann. Statist. , vol.30 , pp. 325-396
    • Hoffmann, M.1    Lepski, O.2
  • 23
    • 0003058689 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives. I, II, III
    • MR1257978, MR1257983, MR1259685
    • INGSTER, YU. I. (1993). Asymptotically minimax hypothesis testing for nonparametric alternatives. I, II, III. Math. Methods Statist. 2 85-114, 171-189, 249-268. MR1257978, MR1257983, MR1259685
    • (1993) Math. Methods Statist. , vol.2 , pp. 85-114
    • Ingster, Yu.I.1
  • 25
    • 33744802846 scopus 로고    scopus 로고
    • Nonparametric confidence set estimation
    • MR2054156
    • JUDITSKY, A. and LAMBERT-LACROIX, S. (2003). Nonparametric confidence set estimation. Math. Methods Statist. 12 410-428. MR2054156
    • (2003) Math. Methods Statist. , vol.12 , pp. 410-428
    • Juditsky, A.1    Lambert-Lacroix, S.2
  • 26
    • 0030490121 scopus 로고    scopus 로고
    • Efficient estimation of integral functional of a density
    • MR1394981
    • LAURENT, B. (1996). Efficient estimation of integral functional of a density. Ann. Statist. 24 659-681. MR1394981
    • (1996) Ann. Statist. , vol.24 , pp. 659-681
    • Laurent, B.1
  • 27
    • 33744779835 scopus 로고    scopus 로고
    • Estimation of integral functional of a density and its derivatives
    • MR1466306
    • LAURENT, B. (1997). Estimation of integral functional of a density and its derivatives. Bernoulli 3 181-211. MR1466306
    • (1997) Bernoulli , vol.3 , pp. 181-211
    • Laurent, B.1
  • 28
    • 0034287154 scopus 로고    scopus 로고
    • Adaptive estimation of a quadratic functional by model selection
    • MR1805785
    • LAURENT, B. and MASSART, P. (2000). Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 1302-1338. MR1805785
    • (2000) Ann. Statist. , vol.28 , pp. 1302-1338
    • Laurent, B.1    Massart, P.2
  • 29
    • 0000012624 scopus 로고
    • On a problem of adaptive estimation in Gaussian white noise
    • MR1091202
    • LEPSKII, O. (1990). On a problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 454-466. MR1091202
    • (1990) Theory Probab. Appl. , vol.35 , pp. 454-466
    • Lepskii, O.1
  • 30
    • 0001066342 scopus 로고
    • Asymptotically minimax adaptive estimation. I. Upper bounds. Optimally adaptive estimates
    • MR1147167
    • LEPSKII, O. (1991). Asymptotically minimax adaptive estimation. I. Upper bounds. Optimally adaptive estimates. Theory Probab. Appl. 36 682-697. MR1147167
    • (1991) Theory Probab. Appl. , vol.36 , pp. 682-697
    • Lepskii, O.1
  • 31
    • 0007267891 scopus 로고
    • Asymptotically minimax adaptive estimation. II. Schemes without optimal adaptation. Adaptive estimates
    • MR1214353
    • LEPSKII, O. (1992). Asymptotically minimax adaptive estimation. II. Schemes without optimal adaptation. Adaptive estimates. Theory Probab. Appl. 37 433-448. MR1214353
    • (1992) Theory Probab. Appl. , vol.37 , pp. 433-448
    • Lepskii, O.1
  • 32
    • 0040276000 scopus 로고
    • Honest confidence regions for nonparametric regression
    • MR1015135
    • LI, K.-C. (1989). Honest confidence regions for nonparametric regression. Ann. Statist. 17 1001-1008. MR1015135
    • (1989) Ann. Statist. , vol.17 , pp. 1001-1008
    • Li, K.-C.1
  • 33
    • 38248998617 scopus 로고
    • A weak invariance principle for weighted U-statistics with varying kernels
    • MR1239107
    • MIKOSCH, T. (1993). A weak invariance principle for weighted U-statistics with varying kernels. J. Multivariate Anal. 47 82-102. MR1239107
    • (1993) J. Multivariate Anal. , vol.47 , pp. 82-102
    • Mikosch, T.1
  • 34
    • 0000912101 scopus 로고
    • Spline smoothing in regression models and asymptotic efficiency
    • MR0803753
    • 2. Ann. Statist. 13984-997. MR0803753
    • (1985) 2. Ann. Statist. , vol.13 , pp. 984-997
    • Nussbaum, M.1
  • 35
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • MR1425959
    • NUSSBAUM, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430. MR1425959
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 36
    • 0000056062 scopus 로고
    • Optimal filtering of square-integrable signals in Gaussian noise
    • MR0624591
    • PINSKER, M. (1980). Optimal filtering of square-integrable signals in Gaussian noise. Problems Inform. Transmission 16 120-133. MR0624591
    • (1980) Problems Inform. Transmission , vol.16 , pp. 120-133
    • Pinsker, M.1
  • 37
    • 0001048793 scopus 로고
    • An asymptotically optimal window selection rule for kernel density estimates
    • MR0760688
    • STONE, C. J. (1984). An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist. 12 1285-1297. MR0760688
    • (1984) Ann. Statist. , vol.12 , pp. 1285-1297
    • Stone, C.J.1


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