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Minimum distance density-based estimation. (English) Zbl 0875.62157

Summary: 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 \(D(f_n,f_\theta)\) between a kernel estimator \(f_n\) 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 \(f_n\). 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.

MSC:

62G07 Density estimation
62F10 Point estimation
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