Abstract
This paper considers a linear-quadratic Tobit regression model, which is developed for modelling the mixture structure with a line segment and a quadratic segment intersecting at an unknown change point. Due to the smoothness of such model structure, the regression coefficients and the change point can be obtained by directly maximising the likelihood function. The proposed estimator has rapid convergence rate and high estimation accuracy, without other computation burden. The asymptotic properties for the proposed estimator are derived by using empirical process theory. A sup-likelihood ratio test procedure is developed for testing the existence of a change point, and its limiting distributions are derived. The good finite sample performances of the proposed estimator are illustrated by numerical studies and empirical applications to the MGUS and GDP data.
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