A CONSTRAINED MAXIMUM-LIKELIHOOD APPROACH TO ESTIMATING SWITCHING REGRESSIONS

It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameters, and if the true parameters satisfy the constraints, there is a global maximizer of the likelihood function on the constrained parameter space which is consistent, asymptotically normal, and efficient. A well-known EM algorithm is modified in order to compute constrained maximizers of the likelihood function.