Two-directional simultaneous inference for high-dimensional models

TL;DR

This paper introduces a two-directional simultaneous inference framework for high-dimensional models, enabling precise identification of zero and non-zero parameters while controlling error rates.

Contribution

It develops the TOSI method that performs dual-direction inference in high-dimensional models, with proven asymptotic error control and high power, improving interpretability and prediction.

Findings

TOSI controls Type I error asymptotically at the desired level.

TOSI achieves high testing power approaching one.

TOSI outperforms existing methods in predictive accuracy and interpretability.

Abstract

This paper proposes a general two directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist zeros in the parameter set of nonzeros. As a result, we can exactly identify whether the parameters are zeros, thereby keeping the data structure fully and parsimoniously expressed. We theoretically prove that the proposed TOSI method asymptotically controls the Type I error at the prespecified significance level and that the testing power converges to one. Simulations are conducted to examine the performance of the proposed method in finite sample situations and two real datasets are analyzed. The results show that the TOSI method is more predictive and has more interpretable estimators than existing methods.