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ABSTRACT:
SUBMITTER: Seregin A
PROVIDER: S-EPMC3058562 | biostudies-literature | 2010 Dec
REPOSITORIES: biostudies-literature
Seregin Arseni A Wellner Jon A JA
Annals of statistics 20101201 6
We study estimation of multivariate densities p of the form p(x) = h(g(x)) for x ∈ ℝ(d) and for a fixed monotone function h and an unknown convex function g. The canonical example is h(y) = e(-y) for y ∈ ℝ; in this case, the resulting class of densities [Formula: see text]is well known as the class of log-concave densities. Other functions h allow for classes of densities with heavier tails than the log-concave class.We first investigate when the maximum likelihood estimator p̂ exists for the cl ...[more]