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Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

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Author Info

  • Härdle, W.K.
  • Mammen, E.
  • Müller, M.D.

    (Tilburg University, Center for Economic Research)

Abstract

We consider a generalized partially linear model E(Y|X,T) = G{X'b + m(T)} where G is a known function, b is an unknown parameter vector, and m is an unknown function.The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model: (i) m is linear, i.e. m(t) = t'g for a parameter vector g, (ii) m is a smooth (nonlinear) function.Under linearity (i) it is shown that the test statistic is asymptotically normal. Moreover, for the case of binary responses, it is proved that the bootstrap works asymptotically.Simulations suggest that (in small samples) bootstrap outperforms the calculation of critical values from the normal approximation.The practical performance of the test is shown in applications to data on East--West German migration and credit scoring.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-42.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199642

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Web page: http://center.uvt.nl

Related research

Keywords: linear models;

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References

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  1. repec:wop:humbsf:1995-44 is not listed on IDEAS
  2. V. Lepski & V. Spokoiny, 1995. "Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative," SFB 373 Discussion Papers 1995,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Carroll, R.J. & Fan, Jianqing. & Gijbels, Irene. & Wand, M.P., . "Generalized Partially Linear Single-Index Models," Statistics Working Paper 95010, Australian Graduate School of Management.
  4. J. FAN & Wolfgang HÄRDLE & Enno MAMMEN, 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. O. V. Lepski & V. G. Spokoiny, 1995. "Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative," SFB 373 Discussion Papers 1995,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Burda, Michael C, 1993. "The Determinants of East-West German Migration: Some First Results," CEPR Discussion Papers 764, C.E.P.R. Discussion Papers.
  7. repec:wop:humbsf:1995-38 is not listed on IDEAS
  8. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
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Cited by:
  1. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2001. "Bootstrap Inference in Semiparametric Generalized Additive Models," Finance Working Papers 01-3, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  2. Enno Mammen, 2007. "Comments on: Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(3), pages 462-464, December.

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