Rate optimal estimation with the integration method in the presence of many covariates
For multivariate regressors, integrating the Nadaraya-Watson regression smoother produces estimators of the lower-dimensional marginal components that are asymptotically normally distributed, at the optimal rate of convergence. Some heuristics, based on consistency of the pilot estimator, suggested that the estimator would not converge at the optimal rate of convergence in the presence of more than four covariates. This paper shows first that marginal integration with its internally normalized counterpart leads to rate-optimal estimators of the marginal components. We introduce the necessary modifications and give central limit theorems. Then, it is shown that the method apply also to more general models, in particular we discuss feasible estimation of partial linear models. The proofs reveal that the pilot estimator shall over-smooth the variables to be integrated, and, that the resulting estimator is itself a lower-dimensional regression smoother. Hence, finite sample properties of the estimator are comparable to those of low-dimensional nonparametric regression. Further advantages when starting with the internally normalized pilot estimator are its computational attractiveness and better performance (compared to its classical counterpart) when the covatiates are correlated and nonuniformly distributed. Simulation studies underline the excellent performance in comparison with so far known methods.
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Volume (Year): 95 (2005)
Issue (Month): 2 (August)
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- Andrews, Donald W.K. & Whang, Yoon-Jae, 1990.
"Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality,"
Cambridge University Press, vol. 6(04), pages 466-479, December.
- Donald W.K. Andrews & Yoon-Jae Whang, 1989. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Cowles Foundation Discussion Papers 925, Cowles Foundation for Research in Economics, Yale University.
- Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 197-251, April.
- Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 1998. "Nonparametric estimation and testing of interaction in additive models," SFB 373 Discussion Papers 1998,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Yang, Lijian & Tjostheim, Dag & Sperlich, Stefan, 1999. "Nonparametric estimation and testing of interaction in additive models," DES - Working Papers. Statistics and Econometrics. WS 6387, Universidad Carlos III de Madrid. Departamento de Estadística.
- 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.
- Enno Mammen & Oliver Linton & J Nielsen, 2000. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 2315, London School of Economics and Political Science, LSE Library.
- Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series 386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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.
- 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.
- Hardle, Wolfgang & Linton, Oliver B. & Sperlich, Stefan, 1998. "Integration and Backfitting methods in additive models: finite sample properties and comparison," DES - Working Papers. Statistics and Econometrics. WS 6270, Universidad Carlos III de Madrid. Departamento de Estadística.
- Opsomer, Jan & Ruppert, David, 1997. "Fitting a Bivariate Additive Model by Local Polynomial Regression," Staff General Research Papers Archive 1071, Iowa State University, Department of Economics.
- Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
- Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
- Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, February. Full references (including those not matched with items on IDEAS)