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Threshold Regression With Nonparametric Sample Splitting

Yoonseok Lee, Yulong Wang

Journal of Econometrics, June 2023

Yoonseok Lee

Yoonseok Lee


Yulong Wang

Yulong Wang


This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold.

We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator.

We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. We illustrate empirical relevance of this new model by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery.