The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use mixed integer programming to solve the proposed L0-norm regularization approach in practice and build a link to the commonly used L1-norm regularization approach. A Monte Carlo study is performed to compare the finite sample performances of the proposed L0-penalized convex quantile and expectile regression approaches with the L1-norm regularization approaches. The proposed approach is further applied to benchmark the sustainable development performance of the OECD countries and empirically analyze the accuracy in the dimensionality reduction of variables. The results from the simulation and application illustrate that the proposed L0-norm regularization approach can more effectively address the curse of dimensionality than the L1-norm regularization approach in multidimensional spaces.
翻译:维度的诅咒是公认的非参数估算中的一项挑战。本文件为子变量选择开发了一种新的L0-北位回归法,用于子变量的孔数和预期回归法。我们展示了如何使用混合整数编程来解决拟议的L0-北位回归法在实践中的实际问题,并与常用的L1-北位回归法建立了联系。蒙特卡洛的一项研究将拟议的L0-二元化孔数和预期回归法的有限样本性能与L1-北位回归法进行比较。拟议办法还进一步用于确定经合组织国家的可持续发展绩效的基准,并用经验分析变量的维度减少的准确性。模拟和应用的结果表明,拟议的L0-北位规范法在多维空间比L1-北位正规化法更有效地解决了维度的诅咒。