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Sieve extremum estimation of a semiparametric transformation model

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  • Lin, Yingqian
  • Tu, Yundong

Abstract

This paper considers the estimation of a semiparametric transformation model, Λ(yt,β0)=g(xt)+ut, where Λ(⋅,β0) is a strictly increasing function known up to an ℓ-dimensional parameter β0, g is an unknown link function. Hermite polynomial expansion is used to approximate the link function g, which leads to an extreme estimator for β0 and a plug-in estimator for g. Asymptotic properties of the estimators are established. Simulation results demonstrate that the estimators perform well in finite samples. An example on Canadian occupation prestige is provided to illustrate the practical value of the proposed model.

Suggested Citation

  • Lin, Yingqian & Tu, Yundong, 2020. "Sieve extremum estimation of a semiparametric transformation model," Economics Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:ecolet:v:189:y:2020:i:c:s0165176520300446
    DOI: 10.1016/j.econlet.2020.109020
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    References listed on IDEAS

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    1. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    2. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    3. Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    4. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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    Cited by:

    1. Lin, Yingqian & Tu, Yundong, 2021. "On transformed linear cointegration models," Economics Letters, Elsevier, vol. 198(C).
    2. Lin, Yingqian & Tu, Yundong, 2024. "Functional coefficient cointegration models with Box–Cox transformation," Economics Letters, Elsevier, vol. 234(C).

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    More about this item

    Keywords

    Extremum estimation; Hermite polynomials; Semiparametrics; Sieve method; Transformation;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • 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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