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Bootstrap Inference In Semiparametric Generalized Additive Models

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Author Info

  • H rdle, Wolfgang
  • Huet, Sylvie
  • Mammen, Enno
  • Sperlich, Stefan

Abstract

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y X;T) = G{XT + + m1(T1) + + md(Td)}. Here, G is a known link, and are unknown parameters, and m1, , md are unknown (smooth) functions of possibly higher dimensional covariates T1, ,Td. Estimates of m1, , md, , and are presented, and asymptotic distributions are given for both the nonparametric and the parametric part. The main focus of the paper is application of bootstrap methods. It is shown how bootstrap can be used for bias correction, hypothesis testing (e.g., component-wise analysis), and the construction of uniform confidence bands. Further, bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of the methods is illustrated in a simulation study.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 20 (2004)
Issue (Month): 02 (April)
Pages: 265-300

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Handle: RePEc:cup:etheor:v:20:y:2004:i:02:p:265-300_20

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  1. 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.
  2. Oliver Linton & E. Mammen & J. Nielsen, 1999. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 300, London School of Economics and Political Science, LSE Library.
  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.
  4. 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.
  5. 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.
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  7. 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.
  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.
  9. Wolfgang Haerdle & Enno MAMMEN & Isabel Proenca, 2005. "A Bootstrap Test for Single Index Models," Econometrics 0508007, EconWPA.
  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. repec:wop:humbsf:1998-3 is not listed on IDEAS
  12. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
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Citations

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Cited by:
  1. 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.
  2. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1286-1296, December.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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).
  11. 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.
  12. 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.

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