Semi‐linear mode regression
提出一种估计半线性回归模型中斜率系数的方法，无需指定非线性部分的函数形式，允许异方差和偏态误差，收敛速度可达n^{-2/7}，并具有oracle性质，蒙特卡洛模拟和长子继承制对经济成就影响的实证分析展示了其优势。
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|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|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.