文章基本信息

标题：Univariate log-concave density estimation with symmetry or modal constraints
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作者：Charles R. Doss ; Jon A. Wellner
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：2391-2461
DOI：10.1214/19-EJS1574
语种：English
出版社：Institute of Mathematical Statistics
摘要：We study nonparametric maximum likelihood estimation of a log-concave density function $f_{0}$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_{0}$ is known, or (b) $f_{0}$ is known to be symmetric about a fixed point $m$. We develop asymptotic theory for both constrained log-concave maximum likelihood estimators (MLE’s), including consistency, global rates of convergence, and local limit distribution theory. In both cases, we find the MLE’s pointwise limit distribution at $m$ (either the known mode or the known center of symmetry) and at a point $x_{0}\ne m$. Software to compute the constrained estimators is available in the R package logcondens.mode.