By Fabienne Comte∗, Valentine Genon-Catalot∗ Université de Paris, MAP5, CNRS, F-75006, France ∗ We considerN independent stochastic processes (Xi(t), t ∈ [0, T ]), i = 1, . . . , N , de ned by a one-dimensional stochastic di erential equation which are continuously observed throughout a time interval [0, T ] where T is xed. We study nonparametric estimation of the drift function on a given subset A of R. Projection estimators are de ned on nite dimensional subsets of L(A, dx). We stress that the set A may be compact or not and the di usion coe cient may be bounded or not. A data-driven procedure to select the dimension of the projection space is proposed where the dimension is chosen within a random collection of models. Upper bounds of risks are obtained, the assumptions are discussed and simulation experiments are reported.

中文翻译：

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随机微分方程iid路径的非参数漂移估计

作者：Fabienne Comte∗, Valentine Genon-Catalot∗ Université de Paris, MAP5, CNRS, F-75006, France ∗ 我们考虑 N 个独立的随机过程 (Xi(t), t ∈ [0, T ]), i = 1, ... . . , N ，由一维随机微分方程定义，该方程在整个时间间隔 [0, T ] 内连续观察，其中 T 是固定的。我们研究了 R 的给定子集 A 上漂移函数的非参数估计。投影估计器定义在 L(A, dx) 的有限维子集上。我们强调集合 A 可能是紧的，也可能不是，扩散系数可能是有界的，也可能是无界的。提出了一种选择投影空间维度的数据驱动程序，其中维度是在模型的随机集合中选择的。获得了风险的上限，讨论了假设并报告了模拟实验。