Asymptotics of M-estimators in two-phase linear regression models
AbstractThis paper discusses the consistency and limiting distributions of a class of M-estimators in two-phase random design linear regression models where the regression function is discontinuous at the change-point with a fixed jump size. The consistency rate of an M-estimator for the change-point parameter r is shown to be n while it is n1/2 for the coefficient parameter estimators, where n denotes the sample size. The normalized M-process is shown to be uniformly locally asymptotically equivalent to the sum of a quadratic form in the coefficient parameter vector and a jump point process in the change-point parameter, in probability. These results are then used to obtain the joint weak convergence of the M-estimators. In particular, is shown to converge weakly to a random variable which minimizes a compound Poisson process, a suitably standardized coefficient parameter M-estimator vector is shown to be asymptotically normal, and independent of .
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 103 (2003)
Issue (Month): 1 (January)
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