ABSTRACT In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.

中文翻译：

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改进了连续时间 Lévy 非参数回归的稳健模型选择方法

摘要 在本文中，我们开发了 James-Stein 改进方法，用于在连续时间内观察到 Lévy 噪声的非参数周期函数的估计问题。构建了基于加权改进最小二乘估计的自适应模型选择程序。研究了非参数模型的改进效果。事实证明，在非渐近设置中，非参数模型的精度改进比参数模型更重要。此外，已经显示了鲁棒风险的尖锐预言不等式，并且已经建立了所提出程序的自适应效率属性。给出了数值模拟。