TL;DR本文提出了一种用于估计对数凹密度函数的最大似然估计方法,该方法利用了计算几何和 Shor 的 r 算法,具有自动化和无需参数选择等优点,并证明了其表现优于基于核的方法,可用于有限混合物拟合。
Abstract
Let X_1, ..., X_n be independent and identically distributed random vectors
with a log-concave (Lebesgue) density f. We first prove that, with probability
one, there exists a unique maximum likelihood estimator of f. The use of this
estimator is attractive because, unlike kernel densit