LEAST ABSOLUTE DEVIATION ESTIMATION OF A SHIFT

This paper develops the asymptotic theory for least absolute deviation estimation of a shift in linear regressions. Rates of convergence and asymptotic distributions for the estimated regression parameters and the estimated shift point are derived. The asymptotic theory is develo ped both for fixed magnitude of shift and for shift with magnitude con verging to zero as the sample size increases. Asymptotic distributions are also obtained for trending regressors and for dependent disturban ces. The analysis is carried out in the framework of partial structura l change, allowing some parameters not to be influenced by the shift. Efficiency relative to least-squares estimation is also discussed. Mon te Carlo analysis is performed to assess how informative the asymptoti c distributions are.