Robust estimation of change points in linear spline models with missing data

Xiang Xiao, Guangyu Yang and Min Zhang

Scandinavian Journal of Statistics, 2026, vol. 53, issue 2, 883-918

Abstract: The estimation of points at which regression coefficients change has attracted considerable interest across many research fields. As in other regression contexts, missing data are ubiquitous. However, while much of the existing literature on missing data focuses on estimating regression coefficients, very few studies address missing data in the context of change point estimation. Linear spline models are powerful tools for studying change points; however, as we demonstrate in simulations, improperly handled missing outcomes can lead to biased estimates of change points. To address this, we propose two novel estimators for change points in linear spline models with potentially missing outcomes: an inverse probability weighting (IPW) estimator and a doubly robust augmented inverse probability weighting (DR‐AIPW) estimator, and study an imputation‐based outcome regression (OR) estimator. We establish the consistency and asymptotic normality of these estimators. Moreover, the DR‐AIPW estimator provides dual protections for consistency, and its optimality is also verified using semi‐parametric theory. We develop two‐step IPW, DR‐AIPW, and OR algorithms for implementation. Simulation studies and real‐data applications demonstrate the strong numerical performance of the proposed estimators.

Date: 2026
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