This paper investigates the Lasso method for sparse linear models with exponential \(\varphi \)-mixing errors under a fixed design, where the number of covariates p is large, or even much larger than the sample size n. The non-asymptotic concentration inequalities for the estimation and prediction errors of the Lasso estimators are given when the errors follow the Gaussian distribution and the sub-exponential distribution, respectively. The prediction and variable selection performance of Lasso estimators are further illustrated through numerical simulations. Finally, the results of the empirical application show that the Index Tracking Fund based on the sparse selection of Lasso can closely track the trend of the target index, and thus provide some useful guidance for the investors.

本文研究了固定设计下具有指数\(\varphi \)混合误差的稀疏线性模型的 Lasso 方法，其中协变量的数量p很大，甚至远大于样本大小n. 当误差分别服从高斯分布和次指数分布时，给出了 Lasso 估计器的估计和预测误差的非渐近浓度不等式。通过数值模拟进一步说明了 Lasso 估计器的预测和变量选择性能。最后，实证应用结果表明，基于Lasso稀疏选择的指数追踪基金可以密切跟踪目标指数的走势，从而为投资者提供一些有益的指导。