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Semiparametric additive indices for binary response and generalized additive models

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  • Härdle, Wolfgang
  • Huet, Sylvie
  • Mammen, Enno
  • Sperlich, Stefan

Abstract

Models are studied where the response Y and covariates X, T are assumed to fulfill E(Y|X; T) = G{XT Ø + » + m1(T1) + … + md(Td)}. Here G is a known (link) function, Ø is an unknown parameter, and m1, …, md are unknown functions. In particular, we consider additive binary response models where the response Y is binary. In these models, given X and T, the response Y has a Bernoulli distribution with parameter G{XT Ø + » + m1(T1) + … + md(Td)}. The paper discusses estimation of Ø and m1, …, md. Procedures are proposed for testing linearity of the additive components m1, …, md. Furthermore, bootstrap uniform confidence intervals for the additive components are introduced. The practical performance of the proposed methods is discussed in simulations and in two economic applications.

Suggested Citation

  • Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 1998. "Semiparametric additive indices for binary response and generalized additive models," SFB 373 Discussion Papers 1998,95, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199895
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    1. Härdle, Wolfgang & Linton, O., 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. 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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    4. Fan, J. & Härdle, Wolfgang & Mammen, Enno, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Andrews, Donald W.K. & Whang, Yoon-Jae, 1990. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Econometric Theory, Cambridge University Press, vol. 6(4), pages 466-479, December.
    6. Proen, I. & Werwatz, A., 1995. "Comparing Parametric and Semiparametric Binary Response Models," SFB 373 Discussion Papers 1995,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
    8. 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.
    9. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
    10. Carroll, R.J. & Fan, Jianqing. & Gijbels, Irene. & Wand, M.P., "undated". "Generalized Partially Linear Single-Index Models," Statistics Working Paper 95010, Australian Graduate School of Management.
    11. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Discussion Paper 1996-42, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Fernández, Ana I. & Rodríguez-Póo, Juan M. & Sperlich, Stefan, 1998. "Semiparametric three step estimation methods in labor supply models," SFB 373 Discussion Papers 1998,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Jorge Barrientos Marin, 2006. "Estimation And Testing An Additive Partially Linear Model In A System Of Engel Curves," Working Papers. Serie AD 2006-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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