  In fitting a mixture of linear regression models, normal assumption is
traditionally used to model the error and then regression parameters are
estimated by the maximum likelihood estimators (MLE). This procedure is not
valid if the normal assumption is violated. To relax the normal assumption on
the error distribution hence reduce the modeling bias, we propose
semiparametric mixture of linear regression models with unspecified error
distributions. We establish a more general identifiability result under weaker
conditions than existing results, construct a class of new estimators, and
establish their asymptotic properties. These asymptotic results also apply to
many existing semiparametric mixture regression estimators whose asymptotic
properties have remained unknown due to the inherent difficulties in obtaining
them. Using simulation studies, we demonstrate the superiority of the proposed
estimators over the MLE when the normal error assumption is violated and the
comparability when the error is normal. Analysis of a newly collected Equine
Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness
of the new estimator.
