DeepAI AI Chat
Log In Sign Up

Uniform Inference in High-Dimensional Generalized Additive Models

by   Philipp Bach, et al.

We develop a method for uniform valid confidence bands of a nonparametric component f_1 in the general additive model Y=f_1(X_1)+... + f_p(X_p) + ε in a high-dimensional setting. We employ sieve estimation and embed it in a high-dimensional Z-estimation framework allowing us to construct uniformly valid confidence bands for the first component f_1. As usual in high-dimensional settings where the number of regressors p may increase with sample, a sparsity assumption is critical for the analysis. We also run simulations studies which show that our proposed method gives reliable results concerning the estimation properties and coverage properties even in small samples. Finally, we illustrate our procedure with an empirical application demonstrating the implementation and the use of the proposed method in practice.


page 1

page 2

page 3

page 4


Lasso Inference for High-Dimensional Time Series

The desparsified lasso is a high-dimensional estimation method which pro...

Post-Regularization Confidence Bands for High Dimensional Nonparametric Models with Local Sparsity

We propose a novel high dimensional nonparametric model named ATLAS whic...

Estimation and inference for high-dimensional nonparametric additive instrumental-variables regression

The method of instrumental variables provides a fundamental and practica...

Estimating Treatment Effect under Additive Hazards Models with High-dimensional Covariates

Estimating causal effects for survival outcomes in the high-dimensional ...

High-dimensional doubly robust tests for regression parameters

After variable selection, standard inferential procedures for regression...

On frequentist coverage errors of Bayesian credible sets in high dimensions

In this paper, we study frequentist coverage errors of Bayesian credible...

Valid Simultaneous Inference in High-Dimensional Settings (with the hdm package for R)

Due to the increasing availability of high-dimensional empirical applica...