Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

arXiv:2004.01623v2 Announce Type: replace-cross
Abstract: We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve estimation into a high-dimensional Z-estimation framework, facilitating the construction of uniformly valid confidence bands for the target component $f_1$. To form these confidence bands, we employ a multiplier bootstrap procedure. Additionally, we provide rates for the uniform lasso estimation in high …

abstract arxiv confidence construct construction econ.em framework inference novel stat.me stat.ml type uniform