Semi-parametric estimation of a generalized threshold regression model under conditional quantile restriction

We consider semi-parametric estimation of a generalized threshold regression model with both the link function and the error term distribution left unspecified. We propose for the model a maximum integrated score estimator (MISE) which allows us to estimate the model under weaker conditional quantile restriction. The MISE is shown to have a convergence rate n-1 for the threshold parameter and a regular n-1/2 rate for the remaining parameters. Moreover, it turns out that the estimates for both parts are asymptotically independent in that their limiting distributions are the same as what they would be if the other part were known. Monte Carlo results indicate that our estimator performs reasonably well in finite samples.