On the Grenander estimator at zero

Mathematics – Statistics Theory

Scientific paper

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28 pages. See also: http://www.stat.washington.edu/www/research/reports/2009/tr554r1 http://www.stat.washington.edu/jaw/RESE

Scientific paper

We establish limit theory for the Grenander estimator of a monotone density
near zero. In particular we consider the situation when the true density $f_0$
is unbounded at zero, with different rates of growth to infinity. In the course
of our study we develop new switching relations by use of tools from convex
analysis. The theory is applied to a problem involving mixtures.

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