M-Estimators of U-Processes With a Change-Point Due to a Covariate Threshold
提出仅利用单调性条件的秩估计量，估计经济理论中的“临界点”和回归系数，并应用于美国四城市社会隔离的临界点估计。
Economic theory often predicts a “tipping point” effect due to multiple equilibria. Linear threshold regressions estimate the “tipping point” by assuming at the same time that the response variable is linear in an index of covariates. However, economic theory rarely imposes a specific functional form, but rather predicts a monotonic relationship between the response variable and the index. We propose new, rank-based, estimators for both the “tipping point” and other regression coefficients, exploiting only the monotonicity condition. We derive the asymptotic properties of these estimators by establishing a more general result for M-estimators of U-processes with a change-point due to a covariate threshold. We finally apply our method to provide new estimates of the “tipping point” of social segregation in four major cities in the United States. Supplementary materials for this article are available online.