报告学生：刘炳圻
报告时间：2022年11月1日
报告文章：Weighted Composite Quantile Regression Inference for Moderate Deviations from a Unit Root Model (Author: Bingqi Liu)
摘要：When studying the moderate deviation process, the most important thing we need to consider is the estimate of q_n and its asymptotic distribution. We know that the ordinary least square is an important and widely used method for estimating model parameters. If the innovation of the model follows a normal distribution, then the OLS estimation is consistent and asymptotically efficient. However, in practical applications, the data usually have the characteristics of biased, leptokurtosis and fat-tail, or have significant heteroscedasticity. At this time, the use of OLS method will make the estimated value more biased and less robust. To this end, {Zhou2015} applied the quantile regression (QR) method proposed by {Koenker 1978} to estimate the parameter q_n of the moderate deviation process and obtain the asymptotic distribution, but this method can lead to arbitrarily small relative efficiency compared with the least squares estimation. To solve this problem, {Ni 2017} used the composite quantile regression (CQR) method proposed by {Zou 2008} to estimate the parameters in the model. As we can see, the CQR method uses the same weight for different quantile. Unfortunately, the same weight is not optimal in general. {Jiang 2012} further proposed a data-driven weighted composite regression method (WCQR) based on CQR, which almost perfectly solves this problem. Motivated by {Jiang 2012}, we use the WCQR method to estimate q_n in different cases when the i.i.d. innovation sequence {u_t} has a second moment which is possibly infinite, deduce the asymptotic distribution containing the weight vector, and then select the optimal weight through a data-driven method.