Semi‐linear mode regression

Jerome M. Krief

Econometrics Journal, 2017, vol. 20, issue 2, 149-167

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.

Date: 2017
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