A new estimator of a jump discontinuity in regression

We propose a new class of estimators for a jump discontinuity on nonparametric regression. While there is a vast literature in econometrics that addresses this issue (e.g., Hahn et al., 2001; Porter, 2003; Imbens and Lemieux, 2008; Cattaneo and Escanciano, 2017), the main approach in these studies is to use local polynomial (linear) estimators on both sides of the discontinuity to produce an estimator for the jump that has desirable boundary properties. Our approach extends the regression from both sides of the discontinuity using a theorem of Hestenes (1941). The extended regressions are then estimated and used to construct an estimator for the jump discontinuity that solves the boundary problems normally associated with classical Nadaraya–Watson estimators. We provide asymptotic characterizations for the jump estimators, including bias and variance orders, and asymptotic distributions after suitable centering and normalization. Monte Carlo simulations show that our jump estimators can outperform those based on local polynomial (linear) regression.