  In this article, we propose a class of semiparametric mixture regression
models with single-index. We argue that many recently proposed
semiparametric/nonparametric mixture regression models can be considered
special cases of the proposed model. However, unlike existing semiparametric
mixture regression models, the new pro- posed model can easily incorporate
multivariate predictors into the nonparametric components. Backfitting
estimates and the corresponding algorithms have been proposed for to achieve
the optimal convergence rate for both the parameters and the nonparametric
functions. We show that nonparametric functions can be esti- mated with the
same asymptotic accuracy as if the parameters were known and the index
parameters can be estimated with the traditional parametric root n convergence
rate. Simulation studies and an application of NBA data have been conducted to
demonstrate the finite sample performance of the proposed models.
