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Bootstrap Inference in Semiparametric Generalized Additive Models

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Author Info
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)

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Abstract

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
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Handle: RePEc:hhb:aarfin:2001_003

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Haerdle, W. & Mammen, E. & Mueller, M., 1996. "Testing parametric versus semiparametric modelling in generalized linear models," Discussion Paper 42, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. E. MAMMEN & S. v. d. GEER, . "Penalized quasi-likelihood estimation in partial linear models," Sonderforschungsbereich 373 1996-6, Humboldt Universitaet Berlin.
  3. 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. [Downloadable!]
  4. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  5. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  6. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
  7. J. Fan & W. H"Ardle & E. Mammen, . "Direct estimation of low dimensional components in additive models," Sonderforschungsbereich 373 1996-17, Humboldt Universitaet Berlin.
  8. 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. [Downloadable!] (restricted)
  9. W. Härdle & E. Mammen & I. Proenca, . "A Bootstrap Test for Single Index Models," Sonderforschungsbereich 373 2000-20, Humboldt Universitaet Berlin.
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  10. 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. [Downloadable!]
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  11. J. Horowitz, . "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Sonderforschungsbereich 373 1998-83, Humboldt Universitaet Berlin.
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  1. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September. [Downloadable!] (restricted)
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