메뉴 건너뛰기




Volumn 41, Issue 4, 2013, Pages 1892-1921

A simple bootstrap method for constructing nonparametric confidence bands for functions

Author keywords

Bandwidth; Bias; Bootstrap; Confidence interval; Conservative coverage; Coverage error; Kernel methods; Statistical smoothing

Indexed keywords


EID: 84885059377     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1137     Document Type: Article
Times cited : (109)

References (60)
  • 1
    • 0000424410 scopus 로고
    • Prepivoting to reduce level error of confidence sets
    • BERAN, R. (1987). Prepivoting to reduce level error of confidence sets. Biometrika 74 457-468.
    • (1987) Biometrika , vol.74 , pp. 457-468
    • Beran, R.1
  • 2
    • 0036489053 scopus 로고    scopus 로고
    • Bayesian smoothing and regression splines for measurement error problems
    • BERRY, S. M., CARROLL, R. J. and RUPPERT, D. (2002). Bayesian smoothing and regression splines for measurement error problems. J. Amer. Statist. Assoc. 97 160-169.
    • (2002) J. Amer. Statist. Assoc. , vol.97 , pp. 160-169
    • Berry, S.M.1    Carroll, R.J.2    Ruppert, D.3
  • 3
    • 3142596617 scopus 로고
    • Uniform confidence bounds for regression based on a simple moving average
    • BJERVE, S., DOKSUM, K. A. and YANDELL, B. S. (1985). Uniform confidence bounds for regression based on a simple moving average. Scand. J. Stat. 12 159-169.
    • (1985) Scand. J. Stat. , vol.12 , pp. 159-169
    • Bjerve, S.1    Doksum, K.A.2    Yandell, B.S.3
  • 4
    • 50449102374 scopus 로고    scopus 로고
    • Variance estimation in nonparametric regression via the difference sequence method
    • BROWN, L. D. and LEVINE, M. (2007). Variance estimation in nonparametric regression via the difference sequence method. Ann. Statist. 35 2219-2232.
    • (2007) Ann. Statist. , vol.35 , pp. 2219-2232
    • Brown, L.D.1    Levine, M.2
  • 5
    • 0000123142 scopus 로고
    • The estimation of residual variance in nonparametric regression
    • BUCKLEY, M. J., EAGLESON, G. K. and SILVERMAN, B. W. (1988). The estimation of residual variance in nonparametric regression. Biometrika 75 189-199.
    • (1988) Biometrika , vol.75 , pp. 189-199
    • Buckley, M.J.1    Eagleson, G.K.2    Silverman, B.W.3
  • 6
    • 55049118453 scopus 로고    scopus 로고
    • Variance function estimation in multivariate non-parametric regression with fixed design
    • CAI, T. T., LEVINE, M. and WANG, L. (2009). Variance function estimation in multivariate non-parametric regression with fixed design. J. Multivariate Anal. 100 126-136.
    • (2009) J. Multivariate Anal. , vol.100 , pp. 126-136
    • Cai, T.T.1    Levine, M.2    Wang, L.3
  • 7
    • 33644903538 scopus 로고    scopus 로고
    • Adaptive confidence balls
    • DOI 10.1214/009053606000000146
    • CAI, T. T. and LOW, M. G. (2006). Adaptive confidence balls. Ann. Statist. 34 202-228. (Pubitemid 43836799)
    • (2006) Annals of Statistics , vol.34 , Issue.1 , pp. 202-228
    • Tony Cai, T.1    Low, M.G.2
  • 8
    • 0011373358 scopus 로고    scopus 로고
    • Empirical likelihood confidence intervals for nonparametric density estimation
    • CHEN, S. X. (1996). Empirical likelihood confidence intervals for nonparametric density estimation. Biometrika 83 329-341.
    • (1996) Biometrika , vol.83 , pp. 329-341
    • Chen, S.X.1
  • 10
    • 1442332685 scopus 로고    scopus 로고
    • Bootstrap confidence bands for regression curves and their derivatives
    • DOI 10.1214/aos/1074290329
    • CLAESKENS, G. and VAN KEILEGOM, I. (2003). Bootstrap confidence bands for regression curves and their derivatives. Ann. Statist. 31 1852-1884. (Pubitemid 38285093)
    • (2003) Annals of Statistics , vol.31 , Issue.6 , pp. 1852-1884
    • Claeskens, G.1    Van Keilegom, I.2
  • 13
    • 73149116074 scopus 로고
    • Confidence bands in nonparametric regression
    • EUBANK, R. L. and SPECKMAN, P. L. (1993). Confidence bands in nonparametric regression. J. Amer. Statist. Assoc. 88 1287-1301.
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 1287-1301
    • Eubank, R.L.1    Speckman, P.L.2
  • 14
    • 0010174211 scopus 로고
    • Confidence regions in non-parametric regression
    • EUBANK, R. L. and WANG, S. (1994). Confidence regions in non-parametric regression. Scand. J. Stat. 21 147-158.
    • (1994) Scand. J. Stat. , vol.21 , pp. 147-158
    • Eubank, R.L.1    Wang, S.2
  • 15
    • 0000871211 scopus 로고    scopus 로고
    • Efficient estimation of conditional variance functions in stochastic regression
    • FAN, J. and YAO, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85 645-660.
    • (1998) Biometrika , vol.85 , pp. 645-660
    • Fan, J.1    Yao, Q.2
  • 16
    • 0001106460 scopus 로고
    • Residual variance and residual pattern in nonlinear regression
    • GASSER, T., SROKA, L. and JENNEN-STEINMETZ, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika 73 625-633.
    • (1986) Biometrika , vol.73 , pp. 625-633
    • Gasser, T.1    Sroka, L.2    Jennen-Steinmetz, C.3
  • 17
    • 22944431500 scopus 로고    scopus 로고
    • Confidence sets for nonparametric wavelet regression
    • DOI 10.1214/009053605000000011
    • GENOVESE, C. R. and WASSERMAN, L. (2005). Confidence sets for nonparametric wavelet regression. Ann. Statist. 33 698-729. (Pubitemid 41053720)
    • (2005) Annals of Statistics , vol.33 , Issue.2 , pp. 698-729
    • Genovese, C.R.1    Wasserman, L.2
  • 18
    • 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
  • 19
    • 77649285528 scopus 로고    scopus 로고
    • Confidence bands in density estimation
    • GINÉ, E. and NICKL, R. (2010). Confidence bands in density estimation. Ann. Statist. 38 1122-1170.
    • (2010) Ann. Statist. , vol.38 , pp. 1122-1170
    • Giné, E.1    Nickl, R.2
  • 20
    • 0001368481 scopus 로고
    • On the bootstrap and confidence intervals
    • HALL, P. (1986). On the bootstrap and confidence intervals. Ann. Statist. 14 1431-1452.
    • (1986) Ann. Statist. , vol.14 , pp. 1431-1452
    • Hall, P.1
  • 21
    • 0001260350 scopus 로고
    • Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density
    • HALL, P. (1992a). 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
  • 22
    • 0000629923 scopus 로고
    • On bootstrap confidence intervals in nonparametric regression
    • HALL, P. (1992b). On bootstrap confidence intervals in nonparametric regression. Ann. Statist. 20 695-711.
    • (1992) Ann. Statist. , vol.20 , pp. 695-711
    • Hall, P.1
  • 24
    • 77956889318 scopus 로고
    • Asymptotically optimal difference-based estimation of variance in nonparametric regression
    • HALL, P., KAY, J. W. and TITTERINGTON, D. M. (1990). Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika 77 521-528.
    • (1990) Biometrika , vol.77 , pp. 521-528
    • Hall, P.1    Kay, J.W.2    Titterington, D.M.3
  • 25
    • 0000035920 scopus 로고
    • On variance estimation in nonparametric regression
    • HALL, P. and MARRON, J. S. (1990). On variance estimation in nonparametric regression. Biometrika 77 415-419.
    • (1990) Biometrika , vol.77 , pp. 415-419
    • Hall, P.1    Marron, J.S.2
  • 26
    • 0012768874 scopus 로고
    • Empirical likelihood confidence bands in density estimation
    • HALL, P. and OWEN, A. B. (1993). Empirical likelihood confidence bands in density estimation. J. Comput. Graph. Statist. 2 273-289.
    • (1993) J. Comput. Graph. Statist. , vol.2 , pp. 273-289
    • Hall, P.1    Owen, A.B.2
  • 27
    • 0000246894 scopus 로고
    • On confidence bands in nonparametric density estimation and regression
    • HALL, P. and TITTERINGTON, D. M. (1988). On confidence bands in nonparametric density estimation and regression. J. Multivariate Anal. 27 228-254.
    • (1988) J. Multivariate Anal. , vol.27 , pp. 228-254
    • Hall, P.1    Titterington, D.M.2
  • 28
    • 84950426508 scopus 로고
    • Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands
    • HÄRDLE, W. and BOWMAN, A. W. (1988). Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands. J. Amer. Statist. Assoc. 83 102-110.
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 102-110
    • Härdle, W.1    Bowman, A.W.2
  • 29
    • 84963386964 scopus 로고
    • Better bootstrap confidence intervals for regression curve estimation
    • HÄRDLE, W., HUET, S. and JOLIVET, E. (1995). Better bootstrap confidence intervals for regression curve estimation. Statistics 26 287-306.
    • (1995) Statistics , vol.26 , pp. 287-306
    • Härdle, W.1    Huet, S.2    Jolivet, E.3
  • 30
    • 0000958548 scopus 로고
    • Bootstrap simultaneous error bars for nonparametric regression
    • HÄRDLE, W. and MARRON, J. S. (1991). Bootstrap simultaneous error bars for nonparametric regression. Ann. Statist. 19 778-796.
    • (1991) Ann. Statist. , vol.19 , pp. 778-796
    • Härdle, W.1    Marron, J.S.2
  • 31
    • 18244426769 scopus 로고    scopus 로고
    • Bootstrap inference in semiparametric generalized additive models
    • DOI 10.1017/S026646660420202X
    • HÄRDLE, W., HUET, S., MAMMEN, E. and SPERLICH, S. (2004). Bootstrap inference in semipara-metric generalized additive models. Econometric Theory 20 265-300. (Pubitemid 38482884)
    • (2004) Econometric Theory , vol.20 , Issue.2 , pp. 265-300
    • Hardle, W.1    Huet, S.2    Mammen, E.3    Sperlich, S.4
  • 32
    • 82655173710 scopus 로고    scopus 로고
    • On adaptive inference and confidence bands
    • HOFFMANN, M. and NICKL, R. (2011). On adaptive inference and confidence bands. Ann. Statist. 39 2383-2409.
    • (2011) Ann. Statist. , vol.39 , pp. 2383-2409
    • Hoffmann, M.1    Nickl, R.2
  • 33
    • 0034991055 scopus 로고    scopus 로고
    • An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative
    • HOROWITZ, J. L. and SPOKOINY, V. G. (2001). An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69 599-631. (Pubitemid 32514244)
    • (2001) Econometrica , vol.69 , Issue.3 , pp. 599-631
    • Horowitz, J.L.1    Spokoiny, V.G.2
  • 34
    • 34250393026 scopus 로고
    • An approximation of partial sums of independent RV's, and the sample DF. II. Z. Wahrsch
    • KOMLÓS, J., MAJOR, P. and TUSNÁDY, G. (1976). An approximation of partial sums of independent RV's, and the sample DF. II. Z. Wahrsch. Verw. Gebiete 34 33-58.
    • (1976) Verw. Gebiete , vol.34 , pp. 33-58
    • Komlós, J.1    Major, P.2    Tusnády, G.3
  • 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
    • 0000918957 scopus 로고
    • Calibrating confidence coefficients
    • LOH, W.-Y. (1987). Calibrating confidence coefficients. J. Amer. Statist. Assoc. 82 155-162.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , pp. 155-162
    • Loh, W.-Y.1
  • 37
    • 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
    • 0000602555 scopus 로고
    • Strong approximation for multivariate empirical and related processes, via KMT constructions
    • MASSART, P. (1989). Strong approximation for multivariate empirical and related processes, via KMT constructions. Ann. Probab. 17 266-291.
    • (1989) Ann. Probab. , vol.17 , pp. 266-291
    • Massart, P.1
  • 39
    • 52749084146 scopus 로고    scopus 로고
    • Bootstrap confidence intervals in nonparametric regression with built-in bias correction
    • MCMURRY, T. L. and POLITIS, D. N. (2008). Bootstrap confidence intervals in nonparametric regression with built-in bias correction. Statist. Probab. Lett. 78 2463-2469.
    • (2008) Statist. Probab. Lett. , vol.78 , pp. 2463-2469
    • Mcmurry, T.L.1    Politis, D.N.2
  • 40
    • 79959703102 scopus 로고    scopus 로고
    • Estimating residual variance in random forest regression
    • MENDEZ, G. and LOHR, S. (2011). Estimating residual variance in random forest regression. Comput. Statist. Data Anal. 55 2937-2950.
    • (2011) Comput. Statist. Data Anal. , vol.55 , pp. 2937-2950
    • Mendez, G.1    Lohr, S.2
  • 41
    • 0037562810 scopus 로고    scopus 로고
    • Estimating the error variance in nonparametric regression by a covariate-matched U-statistic
    • DOI 10.1080/0233188031000078051
    • MÜLLER, U. U., SCHICK, A. and WEFELMEYER, W. (2003). Estimating the error variance in nonparametric regression by a covariate-matched U-statistic. Statistics 37 179-188. (Pubitemid 36761243)
    • (2003) Statistics , vol.37 , Issue.3 , pp. 179-188
    • Muller, U.U.1    Schick, A.2    Wefelmeyer, W.3
  • 42
    • 0000821745 scopus 로고
    • Estimation of heteroscedasticity in regression analysis
    • MÜLLER, H.-G. and STADTMÜLLER, U. (1987). Estimation of heteroscedasticity in regression analysis. Ann. Statist. 15 610-625.
    • (1987) Ann. Statist. , vol.15 , pp. 610-625
    • Müller, H.-G.1    Stadtmüller, U.2
  • 43
  • 44
    • 0000142966 scopus 로고
    • On a semiparametric variance function model and a test for heteroscedasticity
    • MÜLLER, H.-G. and ZHAO, P. L. (1995). On a semiparametric variance function model and a test for heteroscedasticity. Ann. Statist. 23 946-967.
    • (1995) Ann. Statist. , vol.23 , pp. 946-967
    • Müller, H.-G.1    Zhao, P.L.2
  • 46
    • 0000881596 scopus 로고
    • Fully data-driven nonparametric variance estimators
    • NEUMANN, M. H. (1994). Fully data-driven nonparametric variance estimators. Statistics 25 189-212.
    • (1994) Statistics , vol.25 , pp. 189-212
    • Neumann, M.H.1
  • 47
    • 0347706411 scopus 로고
    • Automatic bandwidth choice and confidence intervals in nonparametric regression
    • NEUMANN, M. H. (1995). Automatic bandwidth choice and confidence intervals in nonparametric regression. Ann. Statist. 23 1937-1959.
    • (1995) Ann. Statist. , vol.23 , pp. 1937-1959
    • Neumann, M.H.1
  • 48
    • 0007169427 scopus 로고    scopus 로고
    • Simultaneous bootstrap confidence bands in nonparametric regression
    • NEUMANN, M. H. and POLZEHL, J. (1998). Simultaneous bootstrap confidence bands in nonpara-metric regression. J. Nonparametr. Stat. 9 307-333. (Pubitemid 128547518)
    • (1998) Journal of Nonparametric Statistics , vol.9 , Issue.4 , pp. 307-333
    • Neumann, M.H.1    Polzehl, J.2
  • 49
    • 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
  • 50
    • 0000006440 scopus 로고
    • Bandwidth choice for nonparametric regression
    • RICE, J. (1984). Bandwidth choice for nonparametric regression. Ann. Statist. 12 1215-1230.
    • (1984) Ann. Statist. , vol.12 , pp. 1215-1230
    • Rice, J.1
  • 51
    • 84947934780 scopus 로고
    • An effective bandwidth selector for local least squares regression
    • RUPPERT, D., SHEATHER, S. J. and WAND, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90 1257-1270.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1257-1270
    • Ruppert, D.1    Sheather, S.J.2    Wand, M.P.3
  • 52
    • 21844518517 scopus 로고
    • Multivariate locally weighted least squares regression
    • RUPPERT, D. and WAND, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22 1346-1370.
    • (1994) Ann. Statist. , vol.22 , pp. 1346-1370
    • Ruppert, D.1    Wand, M.P.2
  • 54
    • 0000242067 scopus 로고
    • Improvement of kernel type density estimators
    • SCHUCANY, W. R. and SOMMERS, J. P. (1977). Improvement of kernel type density estimators. J. Amer. Statist. Assoc. 72 420-423.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 420-423
    • Schucany, W.R.1    Sommers, J.P.2
  • 55
    • 0001527882 scopus 로고
    • Nonparametric estimation of residual variance revisited
    • SEIFERT, B., GASSER, T. and WOLF, A. (1993). Nonparametric estimation of residual variance revisited. Biometrika 80 373-383.
    • (1993) Biometrika , vol.80 , pp. 373-383
    • Seifert, B.1    Gasser, T.2    Wolf, A.3
  • 56
    • 21844493366 scopus 로고
    • Simultaneous confidence bands for linear regression and smoothing
    • SUN, J. and LOADER, C. R. (1994). Simultaneous confidence bands for linear regression and smoothing. Ann. Statist. 22 1328-1345.
    • (1994) Ann. Statist. , vol.22 , pp. 1328-1345
    • Sun, J.1    Loader, C.R.2
  • 57
    • 27944441798 scopus 로고    scopus 로고
    • Estimating residual variance in nonparametric regression using least squares
    • DOI 10.1093/biomet/92.4.821
    • TONG, T. and WANG, Y. (2005). Estimating residual variance in nonparametric regression using least squares. Biometrika 92 821-830. (Pubitemid 41681236)
    • (2005) Biometrika , vol.92 , Issue.4 , pp. 821-830
    • Tong, T.1    Wang, Y.2
  • 58
    • 0001866651 scopus 로고
    • A remark on the approximation of the sample DF in the multidimensional case
    • TUSNÁDY, G. (1977). A remark on the approximation of the sample DF in the multidimensional case. Period. Math. Hungar. 8 53-55.
    • (1977) Period. Math. Hungar. , vol.8 , pp. 53-55
    • Tusnády, G.1
  • 59
    • 84963255727 scopus 로고
    • Bootstrap confidence-intervals and for smoothing splines and their comparison to Bayesian confidence-intervals
    • WANG, Y. D. and WAHBA, G. (1995). Bootstrap confidence-intervals and for smoothing splines and their comparison to Bayesian confidence-intervals. Comm. Statist. Simulation Comput. 51 263-279.
    • (1995) Comm. Statist. Simulation Comput. , vol.51 , pp. 263-279
    • Wang, Y.D.1    Wahba, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.