A note on least absolute deviation estimation of a threshold model

This paper develops the limit law for the least absolute deviation estimator of the threshold parameter in linear regression. In this respect, we extend the literature of threshold models. The existing literature considers only the least squares estimation of the threshold parameter (see Chun, 1993, Annals of Statistics 21, 520533; Hansen, 2000, Econometrica 68, 575-605). This result is useful because in the case of heavy-tailed errors there is an efficiency loss resulting from the use of least squares. Also, for the first time in the literature, we derive the limit law for the likelihood ratio test for the threshold parameter using the least absolute deviation technique.