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Maximum pairwise-rank-likelihood-based inference for the semiparametric transformation model

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  • Yu, Tao
  • Li, Pengfei
  • Chen, Baojiang
  • Yuan, Ao
  • Qin, Jing

Abstract

In this paper, we study the linear transformation model in a general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the methods in the literature are based on kernel-smoothing techniques or make use of only the ranks of the responses in the estimation of the parametric components. The former approach needs a tuning parameter, which is not easily optimally specified in practice; and some of the latter may be computationally expensive. In this paper, we propose two methods: a pairwise rank likelihood method and an estimation-equation-based method motivated from the score function of this pairwise rank likelihood. We also explore the theoretical properties of the proposed estimators. Via extensive numerical studies, we demonstrate that our methods are appealing in that the estimators are not only robust to the distribution of the random errors but also lead to mean square errors that are in many cases comparable to or smaller than those of existing methods.

Suggested Citation

  • Yu, Tao & Li, Pengfei & Chen, Baojiang & Yuan, Ao & Qin, Jing, 2023. "Maximum pairwise-rank-likelihood-based inference for the semiparametric transformation model," Journal of Econometrics, Elsevier, vol. 235(2), pages 454-469.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:454-469
    DOI: 10.1016/j.jeconom.2022.05.003
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    References listed on IDEAS

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    1. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
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    11. Chen, Songnian & Zhang, Hanghui, 2020. "n-prediction of generalized heteroscedastic transformation regression models," Journal of Econometrics, Elsevier, vol. 215(2), pages 305-340.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Linear transformation model; M-estimation; Profile likelihood; Pairwise rank likelihood; Pseudo-likelihood; Semiparametric inference;
    All these keywords.

    JEL classification:

    • 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
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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