We study non parametric drift estimation for an ergodic diffusion process from discrete observations. The drift is estimated on a set A using an approximate regression equation by a least squares contrast, minimized over finite dimensional subspaces of ${\mathbb{L}}^2(A,dx)$. The novelty is that the set A is non compact and the diffusion coefficient unbounded. Risk bounds of a ${\mathbb{L}}^2$-risk are provided where new variance terms are exhibited. A data-driven selection procedure is proposed where the dimension of the projection space is chosen within a random set contrary to usual selection procedures.

中文翻译：

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非紧凑型扩散模型支撑的漂移估计

我们从离散观测研究遍历扩散过程的非参数漂移估计。使用近似回归方程通过最小二乘对比度在集合A上估计漂移，并在的有限维子空间上将其最小化${\mathbb{大号}}^2（\mathrm{一种}，dX）$。新颖之处在于集合A是非紧致的，并且扩散系数是无界的。的风险界限${\mathbb{大号}}^2$显示新的方差项时会提供-风险。提出了一种数据驱动的选择程序，其中与常规选择程序相反，在随机集合内选择投影空间的尺寸。