Adaptive wavelet multivariate regression with errors in variables

作者：Chichignoud Michael^*; Hoang Van Ha; Thanh Mai Pham Ngoc; Rivoirard Vincent

来源：Electronic Journal of Statistics, 2017, 11(1): 682-724.

DOI：10.1214/17-EJS1238

• Adaptive wavelet estimator
• anisotropic regression
• deconvolution
• measurement errors

In the multidimensional setting, we consider the errors-invariables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimators based on projection kernels on wavelets and a deconvolution operator. We propose an automatic and fully data driven procedure to select the wavelet level resolution. We obtain an oracle inequality and optimal rates of convergence over anisotropic Holder classes. Our theoretical results are illustrated by some simulations.

• 出版日期2017