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The silhouette, concentration functions and ML-density estimation under order restrictions. (English) Zbl 1073.62523
Summary: Based on empirical Lévy-type concentration functions, a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function to higher dimensions and arbitrary order restrictions. From the given representation it follows that a density estimator called silhouette, which arises naturally out of the excess mass approach, is the ML-density estimator under order restrictions. This fact provides a new point of view to ML-density estimation from which one gains additional insight to this problem, as demonstrated in the present paper.

MSC:
62G07 Density estimation
62F30 Parametric inference under constraints
62G30 Order statistics; empirical distribution functions
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