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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)

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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Bibliographic Info

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

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  1. 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.
  2. 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.
  3. 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.
  4. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
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  6. HÄRDLE, Wolfgang & DIAS PROENCA, sabel M., 1993. "A Bootstrap Test for Single Index Models," CORE Discussion Papers 1993025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. repec:wop:humbsf:1998-3 is not listed on IDEAS
  9. Wolfgang HÄRDLE & Enno MAMMEN & Maike MÜLLER, 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," SFB 373 Discussion Papers 1996,28, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. 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.
  11. 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.
  12. 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.
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Cited by:
  1. Krishna Pendakur & Stefan Sperlich, 2010. "Semiparametric estimation of consumer demand systems in real expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 420-457.
  2. 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.
  3. Roca-Pardinas, Javier & Cadarso-Suarez, Carmen & Tahoces, Pablo G. & Lado, Maria J., 2008. "Assessing continuous bivariate effects among different groups through nonparametric regression models: An application to breast cancer detection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1958-1970, January.
  4. Jing Wang, 2012. "Modelling time trend via spline confidence band," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(2), pages 275-301, April.
  5. Peter Hall & Joel Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. de Uña Álvarez, Jacobo & Roca Pardiñas, Javier, 2009. "Additive models in censored regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3490-3501, July.
  7. Gregory Connor & Thomas Flavin, 2013. "Irish Mortgage Default Optionality," Economics, Finance and Accounting Department Working Paper Series n243-13.pdf, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
  8. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2010. "Direct Simultaneous Inference in Additive Models and its Application to Model Undernutrition," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 50, Courant Research Centre PEG, revised 21 Jul 2011.
  9. 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.
  10. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
  11. Jing Dai & Stefan Sperlich & Walter Zucchini, 2011. "Estimating and Predicting Household Expenditures and Income Distributions," MAGKS Papers on Economics 201147, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
  12. Juan M. Rodríguez-Póo & Stefan Sperlich & Philippe Vieu, 2012. "A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 12093, Institut d'Economie et Econométrie, Université de Genève.

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