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Semi-parametric estimation of generalized partially linear single-index models

Author

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  • Xia, Yingcun
  • Härdle, Wolfgang

Abstract

One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations. In this paper, efficient, constructible and practicable estimators of GPLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. (1997): no root-n pilot estimator for the single index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).

Suggested Citation

  • Xia, Yingcun & Härdle, Wolfgang, 2002. "Semi-parametric estimation of generalized partially linear single-index models," SFB 373 Discussion Papers 2002,56, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200256
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
    3. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
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    Cited by:

    1. Tanha, Hassan & Dempsey, Michael, 2015. "The asymmetric response of volatility to market changes and the volatility smile: Evidence from Australian options," Research in International Business and Finance, Elsevier, vol. 34(C), pages 164-176.
    2. Ormos, Mihály & Timotity, Dusan, 2016. "Unravelling the asymmetric volatility puzzle: A novel explanation of volatility through anchoring," Economic Systems, Elsevier, vol. 40(3), pages 345-354.
    3. Bugge, Sebastian A. & Guttormsen, Haakon J. & Molnár, Peter & Ringdal, Martin, 2016. "Implied volatility index for the Norwegian equity market," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 133-141.
    4. Aboura, Sofiane & Wagner, Niklas, 2016. "Extreme asymmetric volatility: Stress and aggregate asset prices," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 47-59.

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