中文摘要：

在带有罚函数的变量选择中,调节参数的选择是一个关键性问题,但遗憾的是,在大多数文献中,调节参数选择的方法较为模糊,多凭经验,缺乏系统的理论方法。本文基于含随机效应的面板数据模型,提出分位回归中适应性LASSO调节参数的选择标准惩罚交叉验证准则（PCV）,并讨论比较了该准则与其他选择调节参数的准则的效果。通过对不同分位点进行模拟,我们发现当残差ε来自尖峰分布和厚尾分布时,该准则能更好地估计模型参数,尤其对于高分位点和低分位点而言.选取其他分位点时,PCV的效果虽稍逊色于Schwarz信息准则,但明显优于Akaike信息准则和交叉验证准则。且在选择变量的准确性方面,该准则比Schwarz信息准则、Akaike信息准则等更加有效。文章最后对我国各地区多个宏观经济指标的面板数据进行建模分析,展示了惩罚交叉验证准则的性能,得到了在不同分位点处宏观经济指标之间的回归关系。

英文摘要：

Tuning parameter selection plays an important role in variable selection methods with penalty functions. However, it is regrettable that in most literatures, the methods of selecting tuning parameters are vague, lack of systematicness and mostly based on experience. In this paper, panel data with random effects is considered and we propose penalized cross validation for tuning parameter selection in adaptive- LASSO quantile regression. We also compare the different effects on variable selection via PCV and other criteria like SIC, AIC and more. According to simulation results at different quantiles, PCV shows better results on parameters estimation when residual errors follow kurtosis distribution and heavy-tailed distribution, especially at high quantiles and low quantiles. At other quantiles, PCV is slightly inferior to SIC, but has distinct advantages than AIC and CV. As for the accuracy of variable selection, PCV is more efficient than SIC, AIC and CV. Finally, we study the panel data including several maeroeconomic indicators of our country, demonstrate the PCV＇s performance, and get a series of regression models of those macroeconomic indicators at different quantiles.