The asymptotic average squared error for polynomial regression
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Statistics
- Vol. 24 (4) , 311-319
- https://doi.org/10.1080/02331888308802418
Abstract
An asymptotic upper bound is derived for the average expected squared error from polynomial regression. The bound is applied to determine guaranteed rates of convergence for estimation over certain function Classes, Two order selection techniques are shown to be optimal for selecting the number of terms to include in the estimator.Keywords
This publication has 17 references indexed in Scilit:
- A Comparison of a Spline Estimate to its Equivalent Kernel EstimateThe Annals of Statistics, 1991
- Applied Nonparametric RegressionPublished by Cambridge University Press (CUP) ,1990
- Asymptotically optimal difference-based estimation of variance in nonparametric regressionBiometrika, 1990
- Approximation of Least Squares Regression on Nested SubspacesThe Annals of Statistics, 1988
- How Far Are Automatically Chosen Regression Smoothing Parameters From Their Optimum?Journal of the American Statistical Association, 1988
- Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index SetThe Annals of Statistics, 1987
- Residual variance and residual pattern in nonlinear regressionBiometrika, 1986
- Generalized Cross-Validation as a Method for Choosing a Good Ridge ParameterTechnometrics, 1979
- Smoothing noisy data with spline functionsNumerische Mathematik, 1978
- Some Comments on C PTechnometrics, 1973