Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T17:41:57.774Z Has data issue: false hasContentIssue false

LOCALIZED MODEL SELECTION FOR REGRESSION

Published online by Cambridge University Press:  15 January 2008

Yuhong Yang
Affiliation:
University of Minnesota

Abstract

Research on model/procedure selection has focused on selecting a single model globally. In many applications, especially for high-dimensional or complex data, however, the relative performance of the candidate procedures typically depends on the location, and the globally best procedure can often be improved when selection of a model is allowed to depend on location. We consider localized model selection methods and derive their theoretical properties.This research was supported by U.S. National Science Foundation CAREER Grant DMS0094323. We thank three referees and the editors for helpful comments on improving the paper.

Type
Research Article
Copyright
© 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Allen, D.M. (1974) The relationship between variable selection and data augmentation and a method for prediction. Technometrics 16, 125127.Google Scholar
Birgé, L. (1986) On estimating a density using Hellinger distance and some other strange facts. Probability Theory and Related Fields 71, 271291.Google Scholar
Burman, P. (1989) A comparative study of ordinary cross-validation, ν-fold cross-validation and the repeated learning-testing methods. Biometrika 76, 503514.Google Scholar
Geisser, S. (1975) The predictive sample reuse method with applications. Journal of the American Statistical Association 70, 320328.Google Scholar
Kolmogorov, A.N. & V.M. Tihomirov (1959) ε-entropy and ε-capacity of sets in function spaces. Uspehi Mat. Nauk 14, 386.Google Scholar
Li, K.-C. (1987) Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation: Discrete index set. Annals of Statistics 15, 958975.Google Scholar
Pan, W., G. Xiao, & X. Huang (2006) Using input dependent weights for model combination and model selection with multiple sources of data. Statistics Sinica 16, 523540.Google Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. Springer.
Shao, J. (1993) Linear model selection by cross-validation. Journal of the American Statistical Association 88, 486494.Google Scholar
Shao, J. (1997) An asymptotic theory for linear model selection (with discussion). Statistica Sinica 7, 221242.Google Scholar
Stone, M. (1974) Cross-validation choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B 36, 111147.Google Scholar
van de Geer, S. (1993) Hellinger-consistency of certain nonparametric maximum likelihood estimators. Annals of Statistics 21, 1444.Google Scholar
Wegkamp, M.H. (2003) Model selection in nonparametric regression. Annals of Statistics 31, 252273.Google Scholar
Yang, Y. (2007) Consistency of cross validation for comparing regression procedures. Annals of Statistics, forthcoming.Google Scholar
Yang, Y. & A.R. Barron (1999) Information-theoretic determination of minimax rates of convergence. Annals of Statistics 27, 15641599.Google Scholar
Yatracos, Y.G. (1985) Rates of convergence of minimum distance estimators and Kolmogorov's entropy. Annals of Statistics 13, 768774.Google Scholar
Zhang, P. (1993) Model selection via multifold cross validation. Annals of Statistics 21, 299313.Google Scholar