LARGE SYSTEM OF SEEMINGLY UNRELATED REGRESSIONS: A PENALIZED QUASI-MAXIMUM LIKELIHOOD ESTIMATION PERSPECTIVE
针对方程数相对样本量较大的看似无关回归模型，提出惩罚拟极大似然估计量，推导其渐近性质，模拟表明在协方差矩阵稀疏时优于现有方法。
In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate of the estimated covariance matrix in terms of the Frobenius norm. The model selection consistency of the covariance matrix estimator is also established. Simulation results show that when the number of equations is large relative to the sample size and the error covariance matrix is sparse, the PQMLE outperforms other contemporary estimators.