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Multivariate and semiparametric kernel regression

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  • Härdle, Wolfgang
  • Müller, Marlene

Abstract

The paper gives an introduction to theory and application of multivariate and semiparametric kernel smoothing. Multivariate nonparametric density estimation is an often used pilot tool for examining the structure of data. Regression smoothing helps in investigating the association between covariates and responses. We concentrate on kernel smoothing using local polynomial fitting which includes the Nadaraya-Watson estimator. Some theory on the asymptotic behavior and bandwidth selection is provided. In the applications of the kernel technique, we focus on the semiparametric paradigm. In more detail we describe the single index model (SIM) and the generalized partial linear model (GPLM).

Suggested Citation

  • Härdle, Wolfgang & Müller, Marlene, 1997. "Multivariate and semiparametric kernel regression," SFB 373 Discussion Papers 1997,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199726
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    References listed on IDEAS

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    1. Fan, J. & Müller, Maike, 1995. "Density and Regression Smoothing," SFB 373 Discussion Papers 1995,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Hardle, W. & Hall, P. & Marron, J., 1990. "Regression smoothing parameters that are not far from their optimum," LIDAM Discussion Papers CORE 1990009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Marron, J. S. & Nolan, D., 1988. "Canonical kernels for density estimation," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 195-199, December.
    5. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, November.
    6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    7. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, November.
    8. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    9. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
    10. HARDLE, Wolfgang & SCOTT, David, 1990. "Smoothing by weighted averaging of rounded points," LIDAM Discussion Papers CORE 1990040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. 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.
    12. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Other publications TiSEM 3b9b6d39-869e-4ecd-9982-6, Tilburg University, School of Economics and Management.
    13. Carroll, R.J. & Fan, Jianqing. & Gijbels, Irene. & Wand, M.P., "undated". "Generalized Partially Linear Single-Index Models," Statistics Working Paper 95010, Australian Graduate School of Management.
    14. 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.
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    Cited by:

    1. Tomas Ruzgas & Mantas Lukauskas & Gedmantas Čepkauskas, 2021. "Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    2. Dursun AYDIN & Ersin YILMAZ, 2017. "Bandwidth Selection Problem for Nonparametric Regression Model with Right-Censored Data," Romanian Statistical Review, Romanian Statistical Review, vol. 65(2), pages 81-104, June.

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