Estimating the variance in non parametric regression - What is a reasonable choice?

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 60, Issue 4, 1998, Pages 751-764

  Dette, Holger ^a   Munk, Axel ^a   Wagner, Thorsten ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Efficiency; Nonparametric regression; Polynomial weights; Quadratic forms; Variance estimation; Variate difference method

Indexed keywords

EID: 18244372185     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00152     Document Type: Article

References (19)

1. Buckley, M. J. and Eagleson, G. K. (1989) A graphical method for estimating the residual variance in nonparametric regression. Biometrika, 76, 203-210.
2. Buckley, M. J., Eagleson, G. K. and Silverman, B. W. (1988) The estimation of residual variance in non-parametric regression. Biometrika, 75, 189-199.
3. Carroll, R. J. (1987) The effect of variance function estimating on prediction and calibration: an example. In Statistical Decision Theory and Related Topics IV (eds J. O. Berger and S. S. Gupta), vol. II. Heidelberg: Springer.
4. Carroll, R. J. and Ruppert, D. (1988) Transforming and Weighting in Regression. London: Chapman and Hall.
5. Carter, C. K. and Eagleson, G. K. (1992) A comparison of variance estimators in nonparametric regression. J. R. Statist. Soc. B, 54, 773-780.
6. Carter, C. K., Eagleson, G. K. and Silverman, B. W. (1992) A comparison of the Reinsch and Speckman splines. Biometrika, 79, 81-91.
7. Dette, H., Munk, A. and Wagner, T. (1997) A review of variance estimators with extensions to multivariate nonparametric regression models. In Multivariate Design and Sampling (ed. S. Gosh). New York: Dekker. To be published.
8. Eagleson, G. K. (1989) Curve estimation - whatever happened to the variance? Proc. 47th Sess. Int. Statist. Inst., 535-551.
9. Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986) Residual variance and residual pattern in nonlinear regression. Biometrika, 73, 625-633.
10. Hall, P. and Carroll, R. J. (1989) Variance function estimation in regression: the effect of estimating the mean. J. R. Statist. Soc. B, 51, 3-14.
11. Hall, P., Kay, J. W. and Titterington, D. M. (1990) Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika, 77, 521-528.
12. Hall, P. and Marron, J. S. (1990) On variance estimation in nonparametric regression. Biometrika, 77, 415-419.
13. Mathai, A. M. and Provost, S. B. (1992) Quadratic forms in random variables: theory and applications. New York: Dekker.
14. Müller, H. G. and Stadtmüller, U. (1987) Estimation of heteroscedasticity in regression analysis. Ann. Statist., 15, 610-635.
15. Neumann, M. H. (1994) Fully data-driven nonparametric variance estimators. Statistics, 25, 189-212.
16. Rice, J. (1984) Bandwidth choice for nonparametric kernel regression. Ann. Statist., 12, 1215-1230.
17. Seifert, B., Gasser, T. and Wolf, A. (1993) Nonparametric estimation of residual variance revisited. Biometrika, 80, 373-383.
18. Ullah, A. and Zinde-Walsh, V. (1992) On the estimation of residual variance in nonparametric regression. Nonparam. Statist., 1, 263-265.
19. Wahba, G. (1978) Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. R. Statist. Soc. B, 40, 364-372.