Abstract: Nonlinear random coefficient models are used in many different applications, including population pharmacokinetics and econometrics. We describe the minimum distance method of estimating the distributions of the random coefficients, as a substitute for the traditional least-squares type methods. We prove the consistency of the nonparametric minimum distance estimators and the √n-consistency of the parametric minimum distance estimators. The applications of the new method in some population pharmacokinetic models are presented as examples. Numerical comparison of the minimum distance method and a least-squares type method is also given.
Key words and phrases: Random coefficient models, mixed effects models, minimum distance, population pharmacokinetics, Radon transform.