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Boosting local quasi-likelihood estimators

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Abstract

For likelihood-based regression contexts, including generalized linear models, this paper presents a boosting algorithm for local constant quasi-likelihood estimators. Its advantages are the following: (a) the one-boosted estimator reduces bias in local constant quasi-likelihood estimators without increasing the order of the variance, (b) the boosting algorithm requires only one-dimensional maximization at each boosting step and (c) the resulting estimators can be written explicitly and simply in some practical cases.

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References

  • Bühlmann P. and Yu B. (2003). Boosting with the L 2 loss: regression and classification. Journal of the American Statistical Association 98: 324–339

    Article  MATH  MathSciNet  Google Scholar 

  • Choi E. and Hall P. (1998). On bias reduction in local linear smoothing. Biometrika 85: 333–345

    Article  MATH  MathSciNet  Google Scholar 

  • Fan J. (1999). One-step local quasi-likelihood estimation. Journal of the Royal Statistical Society, Ser. B 61: 927–943

    Article  MATH  Google Scholar 

  • Fan J. and Gijbels I. (1996). Local polynomial modelling and its applications. Chapman and Hall, London

    MATH  Google Scholar 

  • Fan J., Heckman N.E. and Wand M.P. (1995). Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. Journal of the American Statistical Association 90: 141–150

    Article  MATH  MathSciNet  Google Scholar 

  • Freund Y. (1995). Boosting a weak learning algorithm by majority. Information and Computation 121: 256–285

    Article  MATH  MathSciNet  Google Scholar 

  • Freund Y. and Schapire R.E. (1996). Experiments with a new boosting algorithm. In: Saitta, L. (Ed.) Machine Learning: Proceedings of the Thirteenth International Conference, pp 144–156. Morgan Kauffman, San Francisco

    Google Scholar 

  • Friedman J. (2001). Greedy function approximation: a gradient boosting machine. The Annals of Statistics 29: 1189–1232

    Article  MATH  MathSciNet  Google Scholar 

  • Jones M.C., Linton O. and Nielsen J. (1995). A simple bias reduction method for density estimation. Biometrika 82: 327–338

    Article  MATH  MathSciNet  Google Scholar 

  • Loader C.R. (1999). Local regression and likelihood. Springer, New York

    MATH  Google Scholar 

  • Marzio M.D. and Taylor C.C. (2004a). Boosting kernel density estimates: A bias reduction technique? Biometrika 91: 226–233

    Article  MATH  MathSciNet  Google Scholar 

  • Marzio, M. D., Taylor, C. C. (2004b). Multistep kernel regression smoothing by boosting. www.amsta.leeds.ac.uk/~charles/boostreg.pdf, unpublished manuscript.

  • Schapire R.E. (1990). The strength of weak learnability. Machine Learning 5: 313–321

    Google Scholar 

  • Wand M.P. and Jones M.C. (1995). Kernel smoothing. Chapman and Hall, London

    MATH  Google Scholar 

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Correspondence to Masao Ueki.

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Ueki, M., Fueda, K. Boosting local quasi-likelihood estimators. Ann Inst Stat Math 62, 235–248 (2010). https://doi.org/10.1007/s10463-008-0173-5

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  • DOI: https://doi.org/10.1007/s10463-008-0173-5

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