数学
统计
估计
卷积(计算机科学)
回归
回归分析
应用数学
赫米特多项式
计量经济学
人工智能
数学分析
计算机科学
人工神经网络
经济
管理
标识
DOI:10.1016/j.jspi.2024.106168
摘要
In this paper, we consider the following regression model: y(kT/n)=f⋆g(kT/n)+ɛk,k=−n,…,n−1, T fixed, where g is known and f is the unknown function to be estimated. The errors (ɛk)−n≤k≤n−1 are independent and identically distributed centered with finite known variance. Two adaptive estimation methods for f are considered by exploiting the properties of the Hermite basis. We study the quadratic risk of each estimator. If f belongs to Sobolev regularity spaces, we derive rates of convergence. Adaptive procedures to select the relevant parameter inspired by the Goldenshluger and Lepski method are proposed and we prove that the resulting estimators satisfy oracle inequalities for sub-Gaussian ɛ's. Finally, we illustrate numerically these approaches.
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