论文标题
关于扩散模型中漂移函数的拉索估计器
On Lasso estimator for the drift function in diffusion models
论文作者
论文摘要
在本文中，我们研究了扩散设置中漂移成分的拉索估计量的性能。更具体地说，我们考虑了在间隔$ [0，t] $上连续观察到的多元参数扩散模型$ x $，并在稀疏约束下调查了转移估计。我们允许模型的尺寸和参数空间很大。我们获得了用于LASSO估计器的Oracle不等式，并使用浓度不等式得出$ l^2 $ distance的误差，用于扩散过程的线性函数。概率部分基于经验过程理论的要素，尤其是基于链接方法。
In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and investigate drift estimation under sparsity constraints. We allow the dimensions of the model and the parameter space to be large. We obtain an oracle inequality for the Lasso estimator and derive an error bound for the $L^2$-distance using concentration inequalities for linear functionals of diffusion processes. The probabilistic part is based upon elements of empirical processes theory and, in particular, on the chaining method.
