Self Modeling Nonlinear Regression

The paper is concerned with parametric models for populations of curves; i.e. models of the form yi (Z) = f(θ i ; x) + error, i = I, 2, …, n. The shape invariant model f(θ i ; x) = θ0i + θ1i g([x – θ2i /θ3i ) is introduced. If the function g(x) is known, then the θ i may be estimated by nonlinear regression. If g(x) is unknown, then the authors propose an iterative technique for simultaneous determination of the best g(x) and θ i . Generalizations of the shape invariant model to curve resolution are also discussed. Several applications of the method are also presented.