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Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator

In: Exploring Research Frontiers in Contemporary Statistics and Econometrics

Author

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  • Yingcun Xia

    (National University of Singapore, Department of Statistics and Applied Probability and Risk Management Institute)

  • Wolfgang Karl Härdle

    (Humboldt-Universität zu Berlin, C.A.S.E. Centre for Applied Statistics and Economics, School of Business and Economics)

  • Oliver Linton

Abstract

In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result, as we show, from inefficient estimation methods or technical difficulties. Xia et al. (J. Roy. Statist. Soc. B. 64:363–410, 2002) proposed an adaptive method for the multiple-index model, called MAVE. In this chapter we further refine the estimation method. Under some conditions, our estimator of the single-index is asymptotically normal and most efficient in the semi-parametric sense. Moreover, we derive higher-order expansions for our estimator and use them to define an optimal bandwidth for the purposes of index estimation. As a result we obtain a practically more relevant method and we show its superior performance in a variety of applications.

Suggested Citation

  • Yingcun Xia & Wolfgang Karl Härdle & Oliver Linton, 2011. "Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator," Springer Books, in: Ingrid Van Keilegom & Paul W. Wilson (ed.), Exploring Research Frontiers in Contemporary Statistics and Econometrics, chapter 0, pages 229-261, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2349-3_11
    DOI: 10.1007/978-3-7908-2349-3_11
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