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On Adaptive Combination of Regression Estimators

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Abstract

Consider the problem of choosing between two estimators of the regression function, where one estimator is based on stronger assumptions than the other and thus the rates of convergence are different. We propose a linear combination of the estimators where the weights are estimated by Mallows' C L . The adaptive estimator retains the optimal rates of convergence and is an extension of Stein-type estimators considered by Li and Hwang (1984, Ann. Statist., 12, 887-897) and related to an estimator in Burman and Chaudhuri (1999, Ann. Inst. Statist. Math. (to appear)).

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REFERENCES

  • Buja, A., Hastie, T. and Tibshirani, R. (1989). Linear smoothers and additive models (with discussion), Ann. Statist., 17, 453–555.

    Google Scholar 

  • Burman, P. and Chandhuri, P. (1999). A hybrid approach to parametric and nonparametric regression, Ann. Inst. Statist. Math. (to appear).

  • Casella, G. and Hwang, J. T. (1982). Limit expressions for the risk of James-Stein estimators, Canad. J. Statist., 10, 305–309.

    Google Scholar 

  • Golubev, G. K. and Nussbaum, M. (1990). A risk bound in Sobolev class regression, Ann. Statist., 18, 758–778.

    Google Scholar 

  • James, W. and Stein, C. M. (1961). Estimating with quadratic loss, Proc. 4th Berkeley Symp. on Math. Statist. Probab., Vol. 1, 361–380, University of California Press.

    Google Scholar 

  • Kneip, A. (1994). Ordered linear smoothers, Ann. Statist., 22, 835–866.

    Google Scholar 

  • Li, K.-C. (1985). From Stein's unbiased risk estimates to the method of generalized cross-validation, Ann. Statist., 13, 1352–1377.

    Google Scholar 

  • Li, K.-C. (1986). Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing, Ann. Statist., 14, 1101–1112.

    Google Scholar 

  • Li, K.-C. (1987). Asymptotic optimality for CP, CL, cross-validation and generalized cross-validation. Discrete index set, Ann. Statist., 15, 958–976.

    Google Scholar 

  • Li, K.-C. and Hwang, J. T. (1984). The data-smoothing aspect of Stein estimates, Ann. Statist., 12, 887–897.

    Google Scholar 

  • Mallows, C. L. (1973). Some comments on CP, Technometrics, 15, 661–675.

    Google Scholar 

  • Stein, C. M. (1962). Confidence sets for the mean of a multivariate normal distribution (with discussion), J. Roy. Statist. Soc. Ser. B, 24, 265–296.

    Google Scholar 

  • Stein, C. M. (1981). Estimation of the mean of a multivariate normal distribution, Ann. Statist., 9, 1135–1151.

    Google Scholar 

  • Whittle, P. (1960). Bounds for the moments of linear and quadratic forms in independent variables, Theory Probab. Appl., 5, 302–305.

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of California, Evans Hall 3860, Berkeley, CA, 94720-3860, U.S.A.

    Helge Blaker

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  1. Helge Blaker
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Blaker, H. On Adaptive Combination of Regression Estimators. Annals of the Institute of Statistical Mathematics 51, 679–689 (1999). https://doi.org/10.1023/A:1004031129852

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