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Semi‐linear mode regression

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  • Jerome M. Krief

Abstract

In this paper, I estimate the slope coefficient parameter β of the regression model Y = X ′ β + φ ( V ) + e , where the error term e satisfies Mode ( e &7C X , V ) = 0 almost surely and ϕ is an unknown function. It is possible to achieve n − 2 / 7 ‐consistency for estimating β when ϕ is known up to a finite‐dimensional parameter. I present a consistent and asymptotically normal estimator for β, which does not require prescribing a functional form for ϕ, let alone a parametrization. Furthermore, the rate of convergence in probability is equal to at least n − 2 / 7 , and approaches n − 1 / 2 if a certain density is sufficiently differentiable around the origin. This method allows both heteroscedasticity and skewness of the distribution of e &7C X , V . Moreover, under suitable conditions, the proposed estimator exhibits an oracle property, namely the rate of convergence is identical to that when ϕ is known. A Monte Carlo study is conducted, and reveals the benefits of this estimator with fat‐tailed and/or skewed data. Moreover, I apply the proposed estimator to measure the effect of primogeniture on economic achievement.

Suggested Citation

  • Jerome M. Krief, 2017. "Semi‐linear mode regression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 149-167, June.
    • Handle: RePEc:wly:emjrnl:v:20:y:2017:i:2:p:149-167
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    File URL: http://hdl.handle.net/10.1111/ectj.12088
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    Cited by:

    1. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    2. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    3. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    4. Qingyang Liu & Xianzheng Huang & Haiming Zhou, 2024. "The Flexible Gumbel Distribution: A New Model for Inference about the Mode," Stats, MDPI, vol. 7(1), pages 1-16, March.

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