U-estimates are defined as maximisers of objective functions that are U-statistics. As an alternative to M-estimates, U-estimates have been extensively used in linear regression, classification, survival analysis, and many other areas. They may rely on weaker data and model assumptions and be preferred over alternatives. In this article, we investigate penalised variable selection with U-estimates. We propose smooth approximations of the objective functions, which can greatly reduce computational cost without affecting asymptotic properties. We study penalised variable selection using penalties that have been well investigated with M-estimates, including the LASSO, adaptive LASSO, and bridge, and establish their asymptotic properties. Generically applicable computational algorithms are described. Performance of the penalised U-estimates is assessed using numerical studies.

中文翻译：

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带有 U 估计的惩罚变量选择

U 估计被定义为作为 U 统计量的目标函数的最大值。作为 M 估计的替代方法，U 估计已广泛用于线性回归、分类、生存分析和许多其他领域。它们可能依赖较弱的数据和模型假设，并且比替代方案更受欢迎。在本文中，我们使用 U 估计研究惩罚变量选择。我们提出了目标函数的平滑逼近，这可以在不影响渐近特性的情况下大大降低计算成本。我们使用已用 M 估计（包括 LASSO、自适应 LASSO 和桥接）充分研究的惩罚来研究惩罚变量选择，并建立它们的渐近特性。描述了普遍适用的计算算法。