Chernoff's density is log-concave.
نویسندگان
چکیده
We show that the density of Z = argmax{W (t) - t2}, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.
منابع مشابه
Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...
متن کاملGlobal Rates of Convergence in Log-concave Density Estimation by Arlene
The estimation of a log-concave density on Rd represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss functions, and adopt a minimax approach. We first show that no statistical procedure based on a sample of size n can estimate a log-concave density with res...
متن کاملLogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density
In this document we introduce the R package LogConcDEAD (Log-concave density estimation in arbitrary dimensions). Its main function is to compute the nonparametric maximum likelihood estimator of a log-concave density. Functions for plotting, sampling from the density estimate and evaluating the density estimate are provided. All of the functions available in the package are illustrated using s...
متن کاملA note on generating random variables with log-concave densities
We present a black-box style rejection method that is valid for generating random variables with any log-concave density, provided that one knows a mode of the density, which is known only up to a constant factor.
متن کاملApproximation by Log - Concave Distributions with Applications to Regression
We study the approximation of arbitrary distributions P on ddimensional space by distributions with log-concave density. Approximation means minimizing a Kullback–Leibler type functional. We show that such an approximation exists if, and only if, P has finite first moments and is not supported by some hyperplane. Furthermore we show that this approximation depends continuously on P with respect...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
دوره 20 1 شماره
صفحات -
تاریخ انتشار 2014