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Square Density Weighted Average Derivatives Estimation of Single Index Models

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  • Myung Jae Sung

    (Hongik University)

Abstract

This paper proposes an average derivatives estimator for index coefficients under a single index model, which does not require restrictive conditions such as zero boundary density or density trimming that are often adopted in previous studies including Powell, Stock, and Stoker (1989, PSSE) and Hardle and Stoker (1989, HSE), among others. Coefficients are consistently estimable by nonparametric mean regression with square density weighted average derivatives (SWADE). Relaxed requirements for SWADE allow more general applications. The asymptotic distribution of SWADE is equivalent in precision to the aforementioned average derivatives estimators (PSSE and HSE). Monte Carlo simulations show that SWADE outperforms HSE in finite sample but is slightly and weakly outweighed by PSSE. These imply that SWADE allows more flexible applications with relaxed distributional characteristics than PSSE and HSE at the expense of slightly deteriorated behavior in finite sample.

Suggested Citation

  • Myung Jae Sung, 2014. "Square Density Weighted Average Derivatives Estimation of Single Index Models," Korean Economic Review, Korean Economic Association, vol. 30, pages 301-331.
    • Handle: RePEc:kea:keappr:ker-20141231-30-2-05
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    References listed on IDEAS

    as
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    6. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Index Coefficients; Square Density Weighting; Average Derivatives; Kernel; Nonparametric;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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