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Derivative estimation and testing in generalized additive models

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Abstract

Estimation and testing procedures for generalized additive (interaction) model are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets.

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  • 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.
    • Handle: RePEc:cte:wsrepe:10084
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    1. Andrews, Donald W.K. & Whang, Yoon-Jae, 1990. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Econometric Theory, Cambridge University Press, vol. 6(4), pages 466-479, December.
    2. 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.
    3. 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.
    4. Sperlich, Stefan & Zelinka, Jiérí, 2000. "Generalized additive models," SFB 373 Discussion Papers 2000,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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