A note on least absolute deviation estimation of a threshold model. (English) Zbl 1181.62021

Summary: 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 Chan, Ann. Stat. 21, 520–533 (1993); Hansen, Econometrica 68, 575–605 (2000)]. 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, we derive the limit law for the likelihood ratio test for the threshold parameter using the least absolute deviation technique.


62F12 Asymptotic properties of parametric estimators
62F05 Asymptotic properties of parametric tests
62J05 Linear regression; mixed models
62P20 Applications of statistics to economics
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