MINIMUM DISTANCE DENSITY-BASED ESTIMATION

We propose a smoothed version of the well-known minimum distance (MD) method for parametric estimation. Our estimators are defined by minimizing (in the vector of parameters theta) a distance D((f) over cap(n),f(theta)) between a kernel estimator (f) over cap(n) of the underlying density and the assumed model f(theta). The consistency, asymptotic normality and qualitative robustness of the resulting estimates are proved. We also discuss the crucial point of the bandwidth choice in the pilot density estimate (f) over cap(n). A simulation study comparing the performance of our method (in different versions) with that of maximum likelihood is included. The results suggest that the MD density-based estimators could offer an interesting alternative. Two case studies with real data are also considered.