本系演講活動

張志浩 副教授

統計學系

國立政治大學

Time: Oct. 30, 2026(Fri.) 14:00-15:00 (GMT+8)

Venue: Business Building 706

Title: Threshold Boundary Logistic Regression: Estimation, Computation, and Asymptotic Theory

Abstract

This talk studies threshold boundary logistic regression (TBLR) for binary response data, in which an unknown function of multiple covariates partitions the covariate space into two regimes with distinct logistic regression models. The threshold boundary may be finite dimensional or nonlinear, allowing heterogeneous binary-response relationships while retaining regime-specific interpretability. We show that boundary estimation can be reformulated as a weighted classification problem, where pseudo-labels and weights are determined by contrasts between the two logistic losses. This representation leads to a weighted support vector machine (WSVM) estimator that accommodates both finite-dimensional and kernel-based nonlinear boundaries. For finite-dimensional boundaries, we further develop a likelihood-based refinement and show that consistency of the preliminary regime-specific regression estimators alone is sufficient for the boundary estimator to attain the $N^{-1}$ convergence rate. Its normalized limiting behavior is characterized by the argmin of a marked compound-Poisson criterion, while the updated logistic estimators are root-$N$ consistent with oracle first-order distributions. For computation, we combine WSVM-based alternating estimation with mixed-integer programming refinement. Simulation studies and a real-data application illustrate the finite-sample performance and flexibility of the proposed framework.