  Mixture of regression models are useful for regression analysis in
heterogeneous populations where a single regression model may not be
appropriate for the entire population. We study the nonparametric maximum
likelihood estimator (NPMLE) for fitting these models. The NPMLE is based on
convex optimization and does not require prior specification of the number of
mixture components. We establish existence of the NPMLE and prove finite-sample
parametric (up to logarithmic multiplicative factors) Hellinger error bounds
for the predicted density functions. We also provide an effective procedure for
computing the NPMLE without ad-hoc discretization and prove a theoretical
convergence rate under certain assumptions. Numerical experiments on simulated
data for both discrete and non-discrete mixing distributions demonstrate the
remarkable performances of our approach. We also illustrate the approach on two
real datasets.
