Sufficient conditions are given in order to ensure the existence of a sequence of strongly consistent estimators of unknown parameters in a nonlinear regression model. The primary difference between this and earlier work is in the generality of the parameter space. Indeed, the parameter space is assumed to be any separable, completely regular topological space; in particular, this includes all separable metric spaces.
"Consistent Estimators in Nonlinear Regression for a Noncompact Parameter Space." Ann. Statist. 14 (4) 1591 - 1596, December, 1986. https://doi.org/10.1214/aos/1176350179