Semi-linear mode regression

摘要

In this paper, I estimate the slope coefficient parameter of the regression model Y=X+phi(V)+e, where the error term e satisfies Mode(e|X,V)=0 almost surely and phi is an unknown function. It is possible to achieve n-2/7-consistency for estimating when phi is known up to a finite-dimensional parameter. I present a consistent and asymptotically normal estimator for , which does not require prescribing a functional form for phi, 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|X,V. Moreover, under suitable conditions, the proposed estimator exhibits an oracle property, namely the rate of convergence is identical to that when phi 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.