Abstract
A class of regression model selection criteria for the data with correlated errors is proposed. The proposed class of selection criteria is an estimator of weighted prediction risk. In addition, the proposed selection criteria are the generalizations of several commonly used criteria in statistical analysis. The theoretical and asymptotic properties for the class of criteria are established. Further, in the medium-sample case, the results based on a simulation study are quite consistent with the theoretical ones. The proposed criteria perform well in the simulations. Several applications are also given for a variety of statistical models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics 22: 203–217
Akaike H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19: 716–723
Altman N.S. (1990). Kernel smoothing of data with correlated errors. Journal of the American Statistical Association 85: 749–759
Craven P., Wahba G. (1979). Smoothing noisy data with spline functions. Numerische Mathematik 31: 377–403
Eilers P.H.C., Marx B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science 11: 89–121
Eubank R.L. (1988). Spline smoothing and nonparametric regression. New York, Dekker
Golub G.H., Van Loan C.F. (1993). Matrix computations. Baltimore and London, The Johns Hopkins University Press
Green P.J., Silverman B.W. (1994). Nonparametric regression and generalized linear models: a roughness penalty approach. London, Chapman and Hall
Härdle W., Müller M., Sperlich S., Werwatz A. (2004). Nonparametric and semiparametric models. Berlin, Springer
Hastie T.J., Tibshirani, R. J. (1990). Generalized additive models. New York, Chapman and Hall
Hocking R.R. (1976). The analysis and selection of variables in linear regression. Biometrics 32: 1–49
Li K.C. (1987). Asymptotic optimality for C p , C L , cross-validation and generalized cross-validation: discrete index set. Annals of Statistics 15: 958–975
Opsomer J., Wang Y., Yang Y. (2001). Nonparametric regression with correlated errors. Statistical Science 16: 134–153
O’Sullivan F., Yandell B., Raynor W. (1986). Automatic smoothing of regression function in generalized linear models. Journal of the American Statistical Association 81: 96–103
Rice J. (1984). Bandwidth choice for nonparametric regression. Annals of Statistics 12: 1215–1230
Shibata R. (1981). An optimal selection of regression variables. Biometrika 68: 45–54
Wahba G. (1990). Spline models for observational data. Philadelphia, Society for Industrial and Applied Mathematics
Wang Y. (1998). Smoothing spline models with correlated random errors. Journal of the American Statistical Association 93: 341–348
Wei W.H. (2005). The smoothing parameter, confidence interval and robustness for smoothing splines. Journal of Nonparametric Statistics 17: 613–642
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Wei, W.H. On regression model selection for the data with correlated errors. Ann Inst Stat Math 61, 291–308 (2009). https://doi.org/10.1007/s10463-007-0145-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-007-0145-1