具有固定效应的加权非对称最小二乘回归
Weighted asymmetric least squares regression with fixed-effects
摘要：
固定效应模型估计对响应均值的回归因子效应，这不足以总结存在异方差的变量关系。本文将非对称最小二乘（期望）回归应用到固定效应模型中，提出了一种新的模型：具有固定效应的期望回归模型$(\ERFE).$。$\ERFE$模型采用内变换策略，将随机参数集中到外，并估计了回归效应对响应分布期望值的影响。$\ERFE$模型捕获数据异方差性，并消除回归变量与忽略因子之间的相关性导致的任何偏倚。我们推导了$\ERFE$估计的渐近性质，并提出了其协方差矩阵的稳健估计。我们的模拟表明，$\ERFE$估计是无偏的，优于其竞争对手。我们的真实数据分析显示了它捕获数据异方差的能力（参见我们的R包，\url{github.com/AmBarry/erfe}）。
英文摘要：
The fixed-effects model estimates the regressor effects on the mean of the response, which is inadequate to summarize the variable relationships in the presence of heteroscedasticity. In this paper, we adapt the asymmetric least squares (expectile) regression to the fixed-effects model and propose a new model: expectile regression with fixed-effects $(\ERFE).$ The $\ERFE$ model applies the within transformation strategy to concentrate out the incidental parameter and estimates the regressor effects on the expectiles of the response distribution. The $\ERFE$ model captures the data heteroscedasticity and eliminates any bias resulting from the correlation between the regressors and the omitted factors. We derive the asymptotic properties of the $\ERFE$ estimators and suggest robust estimators of its covariance matrix. Our simulations show that the $\ERFE$ estimator is unbiased and outperforms its competitors. Our real data analysis shows its ability to capture data heteroscedasticity (see our R package, \url{github.com/AmBarry/erfe}).
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