In this paper, we extend the results of Hjort and Pollard (2011) for random quasiconvex criterion functions. That is to say, for quasiconvex objective functions, we can relax the usual assumption of compactness of the parameter space. In addition, for quasiconvex objective functions, we can derive the limit distribution as argmins of the limit objective function without first establishing the root-n consistency of the estimator.