메뉴 건너뛰기




Volumn 14, Issue 4, 2008, Pages 1089-1107

Mixing least-squares estimators when the variance is unknown

Author keywords

Adaptive minimax estimation; Gibbs mixture; Linear regression; Oracle inequalities; Shrinkage estimator

Indexed keywords


EID: 58149358999     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/08-BEJ135     Document Type: Article
Times cited : (14)

References (28)
  • 1
    • 51249190305 scopus 로고
    • Statistical predictor identification
    • MR0286233
    • Akaike, H. (1969). Statistical predictor identification. Ann. Inst. Statist. Math. 22 203-217. MR0286233
    • (1969) Ann. Inst. Statist. Math , vol.22 , pp. 203-217
    • Akaike, H.1
  • 2
    • 58149508551 scopus 로고    scopus 로고
    • Gaussian model selection with unknown variance
    • To appear. arXiv:math/ 0701250v1
    • Baraud, Y., Giraud, C. and Huet, S. (2008). Gaussian model selection with unknown variance. Ann. Statist. To appear. arXiv:math/ 0701250v1.
    • (2008) Ann. Statist
    • Baraud, Y.1    Giraud, C.2    Huet, S.3
  • 4
    • 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
  • 5
    • 0026190366 scopus 로고
    • Minimum complexity density estimation
    • MR1111806
    • Barron, A. and Cover, T. (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.1    Cover, T.2
  • 6
    • 0034360452 scopus 로고    scopus 로고
    • An adaptive compression algorithm in Besov spaces
    • MR1848840
    • Birgé, L. and Massart, P. (2000). An adaptive compression algorithm in Besov spaces. Constr. Approx. 16 1-36. MR1848840
    • (2000) Constr. Approx , vol.16 , pp. 1-36
    • Birgé, L.1    Massart, P.2
  • 8
    • 33847613502 scopus 로고    scopus 로고
    • Minimal penalties for Gaussian model selection
    • Birgé, L. and Massart, P. (2007). Minimal penalties for Gaussian model selection. Probab. Theory Related Fields 138 33-73.
    • (2007) Probab. Theory Related Fields , vol.138 , pp. 33-73
    • Birgé, L.1    Massart, P.2
  • 9
    • 38049043619 scopus 로고    scopus 로고
    • Aggregation for Gaussian regression
    • MR2351101
    • Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Aggregation for Gaussian regression. Ann. Statist. 35 1674-1697. MR2351101
    • (2007) Ann. Statist , vol.35 , pp. 1674-1697
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 12
    • 58149346853 scopus 로고    scopus 로고
    • Devote, R. and Lorentz, G. (1993). Constructive Approximation. New York: Springer. MR1261635
    • Devote, R. and Lorentz, G. (1993). Constructive Approximation. New York: Springer. MR1261635
  • 13
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • MR1311089
    • Donoho, D. and Johnstone, I. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455. MR1311089
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.1    Johnstone, I.2
  • 14
    • 58149328189 scopus 로고    scopus 로고
    • Mixing least-squares estimators when the variance is unknown
    • Technical report. arXiv:0711.0372v1
    • Giraud, C. (2007). Mixing least-squares estimators when the variance is unknown. Technical report. arXiv:0711.0372v1.
    • (2007)
    • Giraud, C.1
  • 15
    • 77956889318 scopus 로고
    • Asymptotically optimal differencebased estimation of variance in nonparametric regression
    • MR1087842
    • Hall, P., Kay, J. and Titterington, D.M. (1990). Asymptotically optimal differencebased estimation of variance in nonparametric regression. Biometrika 77 521-528. MR1087842
    • (1990) Biometrika , vol.77 , pp. 521-528
    • Hall, P.1    Kay, J.2    Titterington, D.M.3
  • 17
    • 0024767930 scopus 로고
    • Quick and easy analysis of unreplicated factorials
    • MR1041567
    • Lenth, R. (1989). Quick and easy analysis of unreplicated factorials. Technometrics 31 469-473. MR1041567
    • (1989) Technometrics , vol.31 , pp. 469-473
    • Lenth, R.1
  • 18
    • 33746478298 scopus 로고    scopus 로고
    • Information theory and mixing least-squares regressions
    • MR2242356
    • Leung, G. and Barron, A. (2006). Information theory and mixing least-squares regressions. IEEE Trans. Inform. Theory 52 3396-3410. MR2242356
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 3396-3410
    • Leung, G.1    Barron, A.2
  • 20
    • 12844249457 scopus 로고    scopus 로고
    • On difference based variance estimation in nonparametric regression when the covariate is high dimensional
    • MR2136637
    • Munk, A., Bissantz, N., Wagner, T. and Freitag, G. (2005). On difference based variance estimation in nonparametric regression when the covariate is high dimensional. J. Roy. Statist. Soc. Ser B 67 19-41. MR2136637
    • (2005) J. Roy. Statist. Soc. Ser B , vol.67 , pp. 19-41
    • Munk, A.1    Bissantz, N.2    Wagner, T.3    Freitag, G.4
  • 21
    • 0000006440 scopus 로고
    • Bandwidth choice for nonparametric kernel regression
    • MR0760684
    • Rice, J. (1984). Bandwidth choice for nonparametric kernel regression. Ann. Statist. 12 1215-1230. MR0760684
    • (1984) Ann. Statist , vol.12 , pp. 1215-1230
    • Rice, J.1
  • 22
    • 27944441798 scopus 로고    scopus 로고
    • Estimating residual variance in nonparametric regression using least squares
    • MR2234188
    • Tong, T. and Wang, Y. (2005). Estimating residual variance in nonparametric regression using least squares. Biometrika 92 821-830. MR2234188
    • (2005) Biometrika , vol.92 , pp. 821-830
    • Tong, T.1    Wang, Y.2
  • 24
    • 0033233737 scopus 로고    scopus 로고
    • Information-theoretic determination of minimax rates of convergence
    • MR1742500
    • Yang, Y. and Barron, A. (1999). Information-theoretic determination of minimax rates of convergence. Ann. Statist. 27 1564-1599. MR1742500
    • (1999) Ann. Statist , vol.27 , pp. 1564-1599
    • Yang, Y.1    Barron, A.2
  • 25
    • 0004599527 scopus 로고    scopus 로고
    • Combining different procedures for adaptive regression
    • MR1790617
    • Yang, Y. (2000). Combining different procedures for adaptive regression. J. Multivariate Anal. 74 135-161. MR1790617
    • (2000) J. Multivariate Anal , vol.74 , pp. 135-161
    • Yang, Y.1
  • 26
    • 0034410225 scopus 로고    scopus 로고
    • Mixing strategies for density estimation
    • MR1762904
    • Yang, Y. (2000). Mixing strategies for density estimation. Ann. Statist. 28 75-87. MR1762904
    • (2000) Ann. Statist , vol.28 , pp. 75-87
    • Yang, Y.1
  • 27
    • 0742271402 scopus 로고    scopus 로고
    • Combining forecasting procedures: Some theoretical results
    • MR2028357
    • Yang, Y. (2004). Combining forecasting procedures: Some theoretical results. Econometric Theory 20 176-222. MR2028357
    • (2004) Econometric Theory , vol.20 , pp. 176-222
    • Yang, Y.1
  • 28
    • 51049105722 scopus 로고    scopus 로고
    • Effect of mean on variance function estimation in nonparametric regression
    • MR2396810
    • Wang, L., Brown, L., Cai, T. and Levine, M. (2008). Effect of mean on variance function estimation in nonparametric regression. Ann. Statist. 36 646-664. MR2396810
    • (2008) Ann. Statist , vol.36 , pp. 646-664
    • Wang, L.1    Brown, L.2    Cai, T.3    Levine, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.