Nonparametric estimation of multivariate convex-transformed densities
多元凸变换密度的非参数估计
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 $P ( {e}^{− y} ) = \{ p = exp ( − g ) : g \kern0.2em \mathrm{is convex} \}$ 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…