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Integration and backfitting methods in additive models-finite sample properties and comparison

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  • Stefan Sperlich
  • Oliver Linton
  • Wolfgang Härdle

Abstract

We examine and compare the finite sample performance of the competing backfitting and integration methods for estimating additive nonparametric regression using simulated data. Although, the asymptotic properties of the integration estimator, and to some extent the backfitting method too, are well understood, its small sample properties are not well investigated. Apart from some small experiments in the above cited papers, there is little hard evidence concerning the exact distribution of the estimates. It is our purpose to provide an extensive finite sample comparison between the backfitting procedure and the integration procedure using simulated data.
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  • 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;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 419-458, December.
    • Handle: RePEc:spr:testjl:v:8:y:1999:i:2:p:419-458
    DOI: 10.1007/BF02595879
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    1. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    2. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    3. W. Härdle & P. Hall, 1993. "On the backfitting algorithm for additive regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(1), pages 43-57, March.
    4. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    5. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    6. Linton, O. B. & Chen, R. & Härdle, Wolfgang, 1995. "An Analysis of Transformations for Additive Nonparanetric Regression," SFB 373 Discussion Papers 1995,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. 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.
    8. repec:cup:etheor:v:11:y:1995:i:2:p:258-89 is not listed on IDEAS
    9. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    10. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    11. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
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    Citations

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    Cited by:

    1. Yang, Lijian & Hardle, Wolfgang, 2000. "Derivative estimation and testing in generalized additive models," DES - Working Papers. Statistics and Econometrics. WS 10084, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Rodriguez Poo, Juan M. & Vieu, Philippe, 2000. "Semiparametric estimation of weak and strong separable models," DES - Working Papers. Statistics and Econometrics. WS 10064, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Jing Dai & Stefan Sperlich & Walter Zucchini, 2011. "Estimating and predicting the distribution of the number of visits to the medical doctor," MAGKS Papers on Economics 201148, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    5. Hengartner, Nicolas W. & Sperlich, Stefan, 2005. "Rate optimal estimation with the integration method in the presence of many covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 246-272, August.
    6. Sukjin Han, 2020. "Nonparametric estimation of triangular simultaneous equations models under weak identification," Quantitative Economics, Econometric Society, vol. 11(1), pages 161-202, January.
    7. Grasshoff, Ulrike & Schwalbach, Joachim, 1999. "Executive pay and corporate financial performance. An exploratiove data analysis," DES - Working Papers. Statistics and Econometrics. WS 6382, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. repec:grz:wpaper:2012-10 is not listed on IDEAS
    9. Fernández, Ana I. & Rodríguez-Póo, Juan M. & Sperlich, Stefan, 1998. "Semiparametric three step estimation methods in labor supply models," SFB 373 Discussion Papers 1998,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Härdle Wolfgang Karl & Silyakova Elena, 2016. "Implied basket correlation dynamics," Statistics & Risk Modeling, De Gruyter, vol. 33(1-2), pages 1-20, September.
    11. Martins-Filho, Carlos & yang, ke, 2007. "Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion," MPRA Paper 39295, University Library of Munich, Germany.
    12. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    13. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.
    14. Stefan Sperlich, 2014. "On the choice of regularization parameters in specification testing: a critical discussion," Empirical Economics, Springer, vol. 47(2), pages 427-450, September.
    15. Graciela Boente & Alejandra Martínez & Matías Salibián-Barrera, 2017. "Robust estimators for additive models using backfitting," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 744-767, October.
    16. Berthold R. Haag, 2008. "Non‐parametric Regression Tests Using Dimension Reduction Techniques," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 719-738, December.
    17. Guo, Zheng-Feng & Shintani, Mototsugu, 2011. "Nonparametric lag selection for nonlinear additive autoregressive models," Economics Letters, Elsevier, vol. 111(2), pages 131-134, May.
    18. Graciela Boente & Alejandra Martínez, 2017. "Marginal integration M-estimators for additive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 231-260, June.
    19. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2014. "Testing for additivity in partially linear regression with possibly missing responses," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 51-61.
    20. Scholz, Michael & Sperlich, Stefan & Nielsen, Jens Perch, 2016. "Nonparametric long term prediction of stock returns with generated bond yields," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 82-96.
    21. Wolfgang Karl Hardle & Elena Silyakova, 2020. "Implied Basket Correlation Dynamics," Papers 2009.09770, arXiv.org.

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