메뉴 건너뛰기




Volumn 32, Issue 5, 2004, Pages 1805-1840

An adaptation theory for nonparametric confidence intervals

Author keywords

Adaptation; Between class modulus; Confidence intervals; Coverage; Expected length; Linear functionals; Minimax estimation; Modulus of continuity; White noise model

Indexed keywords


EID: 24344508204     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000000049     Document Type: Article
Times cited : (90)

References (26)
  • 1
    • 0003577684 scopus 로고    scopus 로고
    • Adapting to unknown sparsity by controlling the false discovery rate
    • Dept. Statistics, Stanford Univ.
    • ABRAMOVICH, F., BENJAMINI, Y., DONOHO, D. and JOHNSTONE, I. (2000). Adapting to unknown sparsity by controlling the false discovery rate. Technical Report 2000-19, Dept. Statistics, Stanford Univ.
    • (2000) Technical Report , vol.2000 , Issue.19
    • Abramovich, F.1    Benjamini, Y.2    Donoho, D.3    Johnstone, I.4
  • 2
    • 24344470806 scopus 로고    scopus 로고
    • Non-asymptotic minimax rates of testing in signal detection
    • BARAUD, Y. (2002). Non-asymptotic minimax rates of testing in signal detection. Bernoulli 8 577-606.
    • (2002) Bernoulli , vol.8 , pp. 577-606
    • 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
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • BROWN, L. D. and LOW, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 5
    • 0141823280 scopus 로고    scopus 로고
    • On modulus of continuity and adaptability in nonparametric functional estimation
    • Dept. Statistics, Univ. Pennsylvania
    • CAI, T. and LOW, M. (2002). On modulus of continuity and adaptability in nonparametric functional estimation. Technical report, Dept. Statistics, Univ. Pennsylvania.
    • (2002) Technical Report
    • Cai, T.1    Low, M.2
  • 6
    • 24344508395 scopus 로고    scopus 로고
    • Adaptive estimation and confidence intervals for convex functions and monotone functions
    • Dept. Statistics, Univ. Pennsylvania
    • CAI, T. and LOW, M. (2003). Adaptive estimation and confidence intervals for convex functions and monotone functions. Technical report, Dept. Statistics, Univ. Pennsylvania.
    • (2003) Technical Report
    • Cai, T.1    Low, M.2
  • 7
    • 24344450737 scopus 로고    scopus 로고
    • Minimax estimation of linear functionals over nonconvex parameter spaces
    • CAI, T. and LOW, M. (2004). Minimax estimation of linear functionals over nonconvex parameter spaces. Ann. Statist. 32 552-576.
    • (2004) Ann. Statist. , vol.32 , pp. 552-576
    • Cai, T.1    Low, M.2
  • 8
    • 21344492321 scopus 로고
    • Statistical estimation and optimal recovery
    • DONOHO, D. L. (1994). Statistical estimation and optimal recovery. Ann. Statist. 22 238-270.
    • (1994) Ann. Statist. , vol.22 , pp. 238-270
    • Donoho, D.L.1
  • 10
    • 0010946490 scopus 로고
    • Geometrizing rates of convergence. I
    • Dept. Statistics, Univ. California, Berkeley
    • DONOHO, D. L. and LIU, R. C. (1987). Geometrizing rates of convergence. I. Technical Report 137, Dept. Statistics, Univ. California, Berkeley.
    • (1987) Technical Report , vol.137
    • Donoho, D.L.1    Liu, R.C.2
  • 11
    • 0000251164 scopus 로고
    • Geometrizing rates of convergence. III
    • DONOHO, D. L. and LIU, R. C. (1991). Geometrizing rates of convergence. III. Ann. Statist. 19 668-701.
    • (1991) Ann. Statist. , vol.19 , pp. 668-701
    • Donoho, D.L.1    Liu, R.C.2
  • 13
    • 0040040083 scopus 로고    scopus 로고
    • New goodness-of-fit tests and their application to nonparametric confidence sets
    • DÜMBGEN, L. (1998). New goodness-of-fit tests and their application to nonparametric confidence sets. Ann. Statist. 26 288-314.
    • (1998) Ann. Statist. , vol.26 , pp. 288-314
    • Dümbgen, L.1
  • 15
    • 24344467234 scopus 로고    scopus 로고
    • Confidence sets for nonparametric wavelet regression
    • Dept. Statistics, Carnegie Mellon Univ.
    • GENOVESE, C. R. and WASSERMAN, L. (2002). Confidence sets for nonparametric wavelet regression. Technical report, Dept. Statistics, Carnegie Mellon Univ.
    • (2002) Technical Report
    • Genovese, C.R.1    Wasserman, L.2
  • 16
    • 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
  • 17
    • 0000958548 scopus 로고
    • Bootstrap simultaneous error bars for nonparametric regression
    • HAR̈DLE, 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
    • Har̈dle, W.1    Marron, J.S.2
  • 18
    • 21844522284 scopus 로고
    • Finite-sample confidence envelopes for shape-restricted densities
    • HENGARTNER, N. W. and STARK, P. B. (1995). Finite-sample confidence envelopes for shape-restricted densities. Ann. Statist. 23 525-550.
    • (1995) Ann. Statist. , vol.23 , pp. 525-550
    • Hengartner, N.W.1    Stark, P.B.2
  • 19
    • 0002282584 scopus 로고
    • Nonparametric estimation of the value of a linear functional in Gaussian white noise
    • IBRAGIMOV, I. A. and HASMINSKII, R. Z. (1984). Nonparametric estimation of the value of a linear functional in Gaussian white noise. Theory Probab. Appl. 29 18-32.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 18-32
    • Ibragimov, I.A.1    Hasminskii, R.Z.2
  • 20
    • 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
  • 21
    • 0006320560 scopus 로고
    • Bias-variance tradeoffs in functional estimation problems
    • LOW, M. G. (1995). Bias-variance tradeoffs in functional estimation problems. Ann. Statist. 23 824-835.
    • (1995) Ann. Statist. , vol.23 , pp. 824-835
    • Low, M.G.1
  • 22
    • 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
  • 23
    • 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
  • 24
    • 84944400469 scopus 로고
    • Length of confidence intervals
    • PRATT, J. W. (1961). Length of confidence intervals. J. Amer. Statist. Assoc. 56 549-567.
    • (1961) J. Amer. Statist. Assoc. , vol.56 , pp. 549-567
    • Pratt, J.W.1
  • 25
    • 38249015835 scopus 로고
    • Affine minimax confidence intervals for a bounded normal mean
    • STARK, P. B. (1992). Affine minimax confidence intervals for a bounded normal mean. Statist. Probab. Lett. 13 39-44.
    • (1992) Statist. Probab. Lett. , vol.13 , pp. 39-44
    • Stark, P.B.1
  • 26
    • 0009089733 scopus 로고
    • Optimal fixed size confidence procedures for a restricted parameter space
    • ZEYTINOGLU, M. and MINTZ, M. (1984). Optimal fixed size confidence procedures for a restricted parameter space. Ann. Statist. 12 945-957.
    • (1984) Ann. Statist. , vol.12 , pp. 945-957
    • Zeytinoglu, M.1    Mintz, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.