Selection Consistency of Lasso-Based Procedures for Misspecified High-Dimensional Binary Model and Random Regressors

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• High-dimensional regression with binary outcomes presents challenges in variable selection.
• Misspecification of the response function can lead to biased or inconsistent parameter estimates.
• Existing methods may struggle with a large number of predictors relative to observations.

Purpose of the Study:

• To develop a robust variable selection procedure for high-dimensional regression with binary responses.
• To address scenarios involving both correctly specified and misspecified parametric models.
• To ensure consistent identification of relevant predictors under general loss functions.

Main Methods:

• A two-step Screening-Selection (SS) procedure is proposed.
• Step 1: Screening and ordering predictors using the Lasso method.
• Step 2: Selecting the optimal predictor subset by minimizing the Generalized Information Criterion (GIC).

Main Results:

• The proposed SS procedure is proven to be consistent.
• The method effectively handles situations with more predictors than observations.
• In semi-parametric cases, common support between true and estimated parameters is consistently identified.

Conclusions:

• The Screening-Selection (SS) procedure offers a robust approach to variable selection in high-dimensional binary regression.
• The method demonstrates consistency and robustness, even with response function misspecification.
• This work provides a unified framework for parametric inference in both correctly specified and misspecified models.