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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).

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  • 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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    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, 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.
    3. 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.
    4. HARDLE, Wolfgang & SCOTT, David, 1990. "Smoothing by weighted averaging of rounded points," CORE Discussion Papers 1990040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Hardle, W. & Hall, P. & Marron, J., 1990. "Regression smoothing parameters that are not far from their optimum," CORE Discussion Papers 1990009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. 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.
    8. Horowitz, J. L. & Härdle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single - Index Models with Discrete Covariates," SFB 373 Discussion Papers 1994,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Marron, J. S. & Nolan, D., 1988. "Canonical kernels for density estimation," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 195-199, December.
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