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Bootstrap Inference in Semiparametric Generalized Additive Models

  • Härdle, Wolfgang

    (Institut für Statistik und Ökonometrie)

  • Huet, Sylvie

    (Institut de recherche Agronomique)

  • Mammen, Enno

    ()

    (Institut für Angewandte Mathematik)

  • Sperlich, Stefan

    (Department de estadística y Econometría)

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y , covariates X, T the model is E(Y | X; T) = G { X T β + α + m1(T1) + . . . + md(Td) }. Here, G is a known link, â, á are unknown parameters, and m1, . . . , md are unknown (smooth) functions of possibly higher dimensional covariates T1, . . . , Td. Estimates of m1, . . . , md, α and β are presented and asymptotic distribution theory for both the non-parametric and the parametric part is given. The main focus is the application of boot-strap methods. It is shown that bootstrap can be used for bias correction, hypothesis testing (e.g. component-wise analysis) and the construction of uniform confidence bands. Various bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of our methods is illustrated in simulations and in an application to East-West German migration.

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Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Working Papers with number 01-3.

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Length: 43 pages
Date of creation: 12 Mar 2001
Date of revision:
Handle: RePEc:hhb:aarfin:2001_003
Contact details of provider: Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
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  1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
  2. Härdle, Wolfgang & Mammen, Enno & Proença, Isabel, 2000. "A bootstrap test for single index models," SFB 373 Discussion Papers 2000,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Michael C. Burda & Wolfgang Härdle & Marlene Müller & Axel Werwatz, 1998. "Semiparametric analysis of German East-West migration intentions: facts and theory," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 525-541.
  4. Fuss, Melvyn & McFadden, Daniel & Mundlak, Yair, 1978. "A Survey of Functional Forms in the Economic Analysis of Production," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 4 McMaster University Archive for the History of Economic Thought.
  5. 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.
  6. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
  7. Wolfgang HÄRDLE & V. SPOKOINY & S. SPERLICH, 1995. "Semiparametric Single Index Versus Fixed Link Function Modelling," SFB 373 Discussion Papers 1995,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. Burda, Michael C., 1993. "The determinants of East-West German migration: Some first results," European Economic Review, Elsevier, vol. 37(2-3), pages 452-461, April.
  9. repec:dgr:kubcen:199642 is not listed on IDEAS
  10. Stefan Sperlich & Oliver Linton & Wolfgang Härdle, 1999. "Integration and backfitting methods in additive models-finite sample properties and comparison," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(2), pages 419-458, December.
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