Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference
Abstract
Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinearly on multivariate state variables. Random Fourier features provide a flexible and computationally efficient approximation to the nonlinear boundary function. A two-stage procedure first estimates the induced regime classification using a smooth surrogate and then refits the structural parameters by hard-threshold OLS. We establish convergence of the first-stage regime classification and show that its estimation error is asymptotically negligible for the second-stage refit, yielding oracle equivalence. We further develop a dependent-multiplier bootstrap Sup-Wald test for detecting the existence of regime effects when the boundary is unidentified under the null, and establish its asymptotic validity. Simulations demonstrate accurate regime recovery, near-oracle performance of the proposed estimator, and satisfactory finite-sample behavior of the Sup-Wald test. An application to postwar U.S. unemployment data provides strong evidence of regime dependence, while the estimated nonlinear change plane identifies a distinct stress regime characterized by significant shifts in short-run unemployment dynamics.
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BibTeX
@misc{liu2026scalable,
title = {{Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference}},
author = {Wei Liu and Shaogao Lv},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13290},
eprint = {2610.13290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13290},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Scalable Nonparametric Change-Plane Regression with Random Features: Estimation and Inference
AU - Wei Liu
AU - Shaogao Lv
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13290
UR - https://arxiv.org/abs/2610.13290
AB - Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinearly on multivariate state variables. Random Fourier features provide a flexible and computationally efficient approximation to the nonlinear boundary function. A two-stage procedure first estimates the induced regime classification using a smooth surrogate and then refits the structural parameters by hard-threshold OLS. We establish convergence of the first-stage regime classification and show that its estimation error is asymptotically negligible for the second-stage refit, yielding oracle equivalence. We further develop a dependent-multiplier bootstrap Sup-Wald test for detecting the existence of regime effects when the boundary is unidentified under the null, and establish its asymptotic validity. Simulations demonstrate accurate regime recovery, near-oracle performance of the proposed estimator, and satisfactory finite-sample behavior of the Sup-Wald test. An application to postwar U.S. unemployment data provides strong evidence of regime dependence, while the estimated nonlinear change plane identifies a distinct stress regime characterized by significant shifts in short-run unemployment dynamics.
ER -