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Regression and contrast estimated based on adaptive regressograms depending on qualitative explanatory variables

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  • Bunke, Olaf
  • Castell, Ernestina

Abstract

This methodological paper discusses the application of 'adaptive' non-parametric procedures for estimating regression functions or contrasts in situations with quantitative regressands and qualitative regressors. We propose to apply an adaptive regressogram, that is the selection of a regressogram estimate among the class of regressograms corresponding to all possible partitions of the regressor range. Our selection criterion is an analog to Mallows's Cp and this allows to state some small sample and asymptotic properties of the adaptive estimator. We also comment on stepwise selection procedures. The details of the procedure are presented in several interesting special cases, e.g. the two-or three-sample problem and the twoway classification. We illustrate there possible improvements over the usual least squares (ANOVA-)estimates.

Suggested Citation

  • Bunke, Olaf & Castell, Ernestina, 1998. "Regression and contrast estimated based on adaptive regressograms depending on qualitative explanatory variables," SFB 373 Discussion Papers 1998,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199820
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    References listed on IDEAS

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    1. Droge Bernd & Georg Thomas, 1995. "On Selecting The Smoothing Parameter Of Least Squares Regression Estimates Using The Minimax Regret Approach," Statistics & Risk Modeling, De Gruyter, vol. 13(1), pages 1-20, January.
    2. Bunke, O. & Droge, B. & Polzehl, J., 1995. "Model Selection, Transformations and Variance Estimation in Nonlinear Regression," SFB 373 Discussion Papers 1995,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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