带乘法噪声回归估计是统计推断的重要方法之一，在计量经济学、生物统计以及大数据处理等领域发挥着关键作用。小波的多尺度结构和时频局部性质使得小波估计器能够在全局误差意义下达到最优收敛阶。然而，小波估计器的尺度参数选取仅仅关注样本容量大小，且全局误差不能反映局部逼近效果。基于此，本项目将利用数据驱动技术研究带乘法噪声回归函数的点态估计问题。. 为了充分利用观测数据信息进行估计器参数自适应优化，构造数据驱动型小波回归估计器，并在局部Hölder条件下分析其点态最优收敛阶。同时，为了进一步克服常规估计器因“维数灾难”而导致的收敛阶问题，深度融合数据驱动和独立结构条件，构造具备独立结构特性的数据驱动型小波回归估计器，给出其在点态意义下的最优收敛阶。本项目的实施将进一步丰富非参数估计的相关理论，并在一定程度上促进回归估计在大数据处理中的广泛应用。

The regression estimation with multiplication noises is one of the important methods in statistical inference. It plays significant roles in econometrics, biological statistics, big data processing and so on. Since wavelets have important properties such as the multiresolution structure and time-frequency localization, wavelet estimators can attain the optimal convergence rates in global error sense. However, the scale parameter selection of wavelet estimators only focus on the sample size, and the global error can not reflect the local approximation effect. This project aims to study pointwise estimations for regression functions with multiplication noises based on data driven. . In order to sufficiently use the observed data information to adaptively optimize the scale parameter of estimators, we construct data driven wavelet estimators, and analyze pointwise optimal convergence rates under local Hölder condition. Moreover, we make deep fusion of data driven and independence structure, construct data driven wavelet estimators with independence structure to overcome the problem of curse of dimensionality, and give the optimal convergence rates in pointwise sense. The implementation of this project will enrich relevant theories of nonparametric estimation, and promote the wide application of regression estimation in big data processing.