Modèle de régression avec variables d’écart

A look at M. G. Dagenais' contributions (1969, 1973) on threshold regression models and at chapter 9 of S.M. Goldfeld and R.E. Quandt's book (1972) concerning switching regression models suggested to me that a new approach to estimating the threshold model by introducing slack variables might be possible. One of the main advantages of this new method is to simplify to a great extent the estimation of the likelihood function which is reduced partly to the problem of estimating a limited number of simple integrals for each iteration in the process of optimization.