The Annals of Statistics
- Ann. Statist.
- Volume 26, Number 5 (1998), 1857-1877.
The silhouette, concentration functions and ML-density estimation under order restrictions
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.
Ann. Statist., Volume 26, Number 5 (1998), 1857-1877.
First available in Project Euclid: 21 June 2002
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Polonik, Wolfgang. The silhouette, concentration functions and ML-density estimation under order restrictions. Ann. Statist. 26 (1998), no. 5, 1857--1877. doi:10.1214/aos/1024691360. https://projecteuclid.org/euclid.aos/1024691360