Relative Errors of Difference-Based Variance Estimators in Nonparametric Regression

References

• Buckley , M. J. , Eagleson , G. K. , Silverman , B. W. ( 1988 ). The estimation of residual variance in non-parametric regression . Biometrika 75 : 189 – 199 .
   Web of Science ®Google Scholar
• Carter , C. K. , Eagleson , G. K. ( 1992 ). A comparison of variance estimations in nonparametric regression . J. Roy. Statist. Soc. B 54 : 773 – 780 .
   Google Scholar
• Dette , H. , Munk , A. , Wagner , T. ( 1998 ). Estimating the variance in nonparametric regression–what is a reasonable choice? J. Roy. Statist. Soc. B 60 : 751 – 764 .
   Google Scholar
• Eagleson , G. K. ( 1989 ). Curve estimation–whatever happened to the variance? Proc. 47th Sess. Int. Statist. Inst. 535 – 551 .
   Google Scholar
• Eubank , R. ( 1999 ). Nonparametric Regression and Spline Smoothing . New York : Dekker .
   Google Scholar
• Gasser , T. , Sroka , L. , Jennen-Steinmetz , C. ( 1986 ). Residual variance and residual pattern in nonlinear regression . Biometrika 73 : 625 – 633 .
   Web of Science ®Google Scholar
• Hall , P. , Marron , J. S. ( 1990 ). On variance estimation in nonparametric regression . Biometrika 77 : 415 – 419 .
   Web of Science ®Google Scholar
• Hall , P. , Kay , J. W. , Titterington , D. M. ( 1990 ). Asymptotically optimal difference-based estimation of variance in nonparametric regression . Biometrika 77 : 521 – 528 .
   Web of Science ®Google Scholar
• Hastie , T. , Tibshirani , R. ( 1990 ). Generalized Additive Models . London : Chapman and Hall .
   Google Scholar
• Müller , U. , Schick , A. , Wefelmeyer , W. ( 2003 ). Estimating the error variance in nonparametric regression by a covariate-matched U-statistic . Statistics 37 : 179 – 188 .
   Web of Science ®Google Scholar
• Munk , A. , Bissantz , N. , Wagner , T. , Freitag , G. ( 2005 ). On difference-based variance estimation in nonparametric regression when the covariate is high dimensional . J. Roy. Statist. Soc. B 67 : 19 – 41 .
   Google Scholar
• Rice , J. A. ( 1984 ). Bandwidth choice for nonparametric regression . Ann. Statist. 12 : 1215 – 1230 .
   Web of Science ®Google Scholar
• Tong , T. , Wang , Y. ( 2005 ). Estimating residual variance in nonparametric regression using least squares . Biometrika 92 : 821 – 830 .
   Web of Science ®Google Scholar
• von Neumann , J. ( 1941 ). Distribution of the ratio of the mean squared successive difference to the variance . Ann. Mathemat. Statist. 12 : 367 – 395 .
   Google Scholar
• Wahba , G. ( 1978 ). Improper priors, spline smoothing and the problem of guarding against model errors in regression . J. Roy. Statist. Soc. B 40 : 364 – 372 .
   Google Scholar
• Wahba , G. ( 1990 ). Spline Models for Observational Data . CBMS-NSF Regional Conference Series in Applied Mathematics , Vol. 59 . Philadelphia : SIAM .
   Google Scholar
• Wand , M. P. , Jones , M. C. ( 1995 ). Kernel Smoothing . London : Chapman and Hall .
   Google Scholar