We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum likelihood estimator (CQMLE) is considered after taking the differences to remove the skewness of noise, and we prove its asymptotic normality and tail-probability estimate; second, as for stable-distribution parameters, we consider the moment estimators based on the symmetrized and centered residuals and prove their $\sqrt{n}$-consistency. To derive the $\sqrt{n}$-consistency, we essentially used the tail-probability estimate of the CQMLE. The proposed estimation procedure has a very low computational load and is much less time-consuming compared with the maximum-likelihood estimator. Further, our estimator can be effectively used as an initial value of the numerical optimization of the log-likelihood.

翻译：我们研究了可能带有偏斜稳定分布误差的线性回归模型的参数估计方法。该估计过程包括两个阶段：首先，针对回归系数，在通过差分消除噪声偏斜后，考虑柯西拟极大似然估计量（CQMLE），并证明了其渐近正态性和尾部概率估计；其次，针对稳定分布参数，我们基于对称化和中心化残差考虑矩估计量，并证明了其$\sqrt{n}$一致性。为推导$\sqrt{n}$一致性，我们本质性地使用了CQMLE的尾部概率估计。所提出的估计过程计算负荷极低，与极大似然估计量相比耗时显著减少。此外，该估计量可作为对数似然数值优化的有效初始值。