Estimation and Uniform Inference in Sparse High-Dimensional Additive Models
This addresses the need for robust statistical inference in high-dimensional data analysis, though it is incremental as it builds on existing methods like sieve estimation and Z-estimation.
The paper tackles the problem of constructing uniformly valid confidence bands for a nonparametric component in sparse high-dimensional additive models, achieving reliable estimation and coverage in simulations, even with small samples.
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 dimensions, which may be of independent interest. Through simulation studies, we demonstrate that our proposed method delivers reliable results in terms of estimation and coverage, even in small samples.