Skip to main content

Nonparametric Approaches to Generalized Linear Models

  • Conference paper
Advances in GLIM and Statistical Modelling

Part of the book series: Lecture Notes in Statistics ((LNS,volume 78))

Abstract

In this paper we consider classes of statistical models that are natural generalizations of generalized linear models. Generalized linear models cover a very broad class of classical statistical models including linear regression, ANOVA, logit, and probit models. An important element of generalized linear models is that they contain parametric components of which the influence has to be determined by the experimentator. Here we describe some lines of thought and research relaxing the parametric structure of these components.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ansley, C.F. and Kohn R. (1991), “Convergence of the Backfitting Algorithm for Additive Models,” Working Paper 91-013, Australian Graduate School of Management.

    Google Scholar 

  • Bierens, H.J. (1990), “A consistent conditional moment test of functional form,” Econometrica, 58, 1443–1458.

    Article  MathSciNet  MATH  Google Scholar 

  • Breiman, L. and Friedman, J.H. (1985), “Estimating optimal transformations for multiple regression and correlation (with discussion),” Journal of the American Statistical Association, 80, 580–619.

    Article  MathSciNet  MATH  Google Scholar 

  • Buja, A., Hastie, T.J. and Tibshirani, R.J. (1989), “Linear smoothers and additive models (with discussion),” The Annals of Statistics, 17, 453–555

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. and Marron, J. S. (1992) “Fast implementations of nonparametric curve estimators”, unpublished manuscript.

    Google Scholar 

  • Friedman, J.H. and Stuetzle, W. (1981), “Projection Pursuit Regression,” Journal of the American Statistical Association, 76, 817–823.

    Article  MathSciNet  Google Scholar 

  • Huber, P.J. (1985), “Projection Pursuit,” The Annals of Statistics, 13, 435–475.

    Article  MathSciNet  MATH  Google Scholar 

  • Härdle, W., Hart J., Marron J.S., and Tsybakov, A.B. (1992), “Bandwidth Choice for Average Derivative Estimation,” Journal of the American Statistical Association, 87, 817–823.

    Article  Google Scholar 

  • Härdle, W. and Hall, P. (1992), “Simple formulae for steps and limits in the backfitting algorithm,” Statistica Neerlandica, to appear.

    Google Scholar 

  • Härdle, W., Hall, P. and Ichimura, H. (1991), “Optimal Smoothing in Single Index Models,” Core Discussion Paper No 9107.

    Google Scholar 

  • Härdle, W. and Scott, D.W. (1992), “Smoothing by Weighted Averaging of Rounded Points,” Computational Statistics, in print.

    Google Scholar 

  • Härdle, W. and Stoker, T.M. (1989), “Investigating Smooth Multiple Regression by the Method of Average Derivatives,” Journal of the American Statistical Association, 84, 986–995.

    Article  MathSciNet  MATH  Google Scholar 

  • Härdle, W. and Tsybakov, A.B. (1991), “How sensitive are average derivatives?,” CORE Discussion Paper No 9144.

    Google Scholar 

  • Hall, P. (1989), “On Projection Pursuit Regression”, The Annals of Statistics, 17, 573–588

    Article  MathSciNet  MATH  Google Scholar 

  • Hastie, T.J. and Tibshirani, R.J. (1987), “Non-parametric Logistic and Proportional Odds Regression,” Applied Statistics, 36, 260–276.

    Article  Google Scholar 

  • Hastie, T.J. and Tibshirani, R.J. (1990), Generalized Additive Models, Chapman and Hall, London.

    MATH  Google Scholar 

  • Horowitz, J. and Härdle, W. (1992), “Testing a parametric model against a semiparametric alternative”, CentER Discussion Paper.

    Google Scholar 

  • Ichimura, H. (1992), “Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models,” Journal of Econometrics, special issue on “Nonparametric Approaches to Discrete Choice Models“, éd. W. Härdle and C.F. Manski.

    Google Scholar 

  • Newey, W.K. (1985), “Maximum likelihood specification testing and conditional moment test,” Econometrica, 53, 1047–1070.

    Article  MathSciNet  MATH  Google Scholar 

  • McCullagh, P. and Nelder, J.A. (1989), Generalized Linear Models, 2nd Edition, Chapman and Hall, London.

    MATH  Google Scholar 

  • Rodriguez-Campos, M.C. and Cao-Abad, R. (1992), “Nonparametric Bootstrap Confidence Intervals for Discrete Regression Functions,” Journal of Econometrics, special issue on “Nonparametric Approaches to Discrete Choice Models”, ed. W. Härdle and C.F. Manski.

    Google Scholar 

  • Scott, D.W. (1985), “Averaged Shifted Histograms: Effective Nonparametric Density Estimators in Several Dimensions,” The Annals of Statistics, 13, 1024–1040

    Article  MathSciNet  MATH  Google Scholar 

  • Silverman, B.W. (1986), ‘Density Estimation for Statistical and Data Analysis, Chapman and Hall, London.

    Google Scholar 

  • Stoker, T.M. (1991), “Equivalence of Direct, Indirect and Slope Estimators of Average Derivatives,” in Nonparametric and Semiparametric Methods in Econometrics and Statistics, Bar-nett, W.A., J.L. Powell and G. Tauchen, eds., Cambridge University Press.

    Google Scholar 

  • Stoker, T.M. (1992a), Lectures on Semiparametrics Econometrics, CORE Lecture Series, Louvain-la-Neuve.

    Google Scholar 

  • Stoker, T.M. and Villas-Boas, J.M. (1992b), “Monte Carlo Simulation of Average Derivative Estimators,” Discussion Paper, Sloan School of Management, MIT.

    Google Scholar 

  • Turlach, B. (1992), “Discretization Methods in high-dimensional smoothing,” CORE Discussion Paper.

    Google Scholar 

  • XploRe (1992), XploRe 3.0 — a computing environment for eXploratory Regression and data analysis. Available from XploRe Systems, C.O.R.E. Université Catholique de Louvain, Belgium.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Härdle, W.K., Turlach, B.A. (1992). Nonparametric Approaches to Generalized Linear Models. In: Fahrmeir, L., Francis, B., Gilchrist, R., Tutz, G. (eds) Advances in GLIM and Statistical Modelling. Lecture Notes in Statistics, vol 78. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2952-0_33

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2952-0_33

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97873-4

  • Online ISBN: 978-1-4612-2952-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics