Decorrelated Local Linear Estimator: Inference for Non-linear Effects in High-dimensional Additive Models

TL;DR

This paper introduces a decorrelated local linear estimator for inference on non-linear effects in high-dimensional additive models, enabling confidence intervals and hypothesis testing with proven asymptotic normality.

Contribution

It proposes a novel decorrelated estimator that effectively reduces estimation error for inference in high-dimensional additive models, including confidence intervals and hypothesis tests.

Findings

Estimator achieves asymptotic normality.

Method performs well in large-scale simulations.

Applied successfully to motif regression analysis.

Abstract

Additive models play an essential role in studying non-linear relationships. Despite many recent advances in estimation, there is a lack of methods and theories for inference in high-dimensional additive models, including confidence interval construction and hypothesis testing. Motivated by inference for non-linear treatment effects, we consider the high-dimensional additive model and make inference for the derivative of the function of interest. We propose a novel decorrelated local linear estimator and establish its asymptotic normality. The main novelty is the construction of the decorrelation weights, which is instrumental in reducing the error inherited from estimating the nuisance functions in the high-dimensional additive model. We construct the confidence interval for the function derivative and conduct the related hypothesis testing. We demonstrate our proposed method over large-scale simulation studies and apply it to identify non-linear effects in the motif regression problem. Our proposed method is implemented in the R package \texttt{DLL} available from CRAN.