Exact solutions in log-concave maximum likelihood estimation

DOI10.1016/j.aam.2022.102448OpenAlexW3012094871MaRDI QIDQ2104907

Yanyan Li

Publication date: 8 December 2022

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04840

zbMATH Keywords

maximum likelihood estimationpolyhedral subdivisionslog-concavitySmale's \(\alpha\)-theorytranscendence theorycertified solutionspolynomial-exponential systemsLambert functions

Mathematics Subject Classification ID

Density estimation (62G07)

Uses Software

• Bertini
• alphaCertified
• LogConcDEAD
• logcondens
• NumericalAlgebraicGeometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• LogConcDEAD
• Global rates of convergence of the MLEs of log-concave and \(s\)-concave densities
• Quantifier elimination for a class of exponential polynomial formulas
• Certifying solutions to square systems of polynomial-exponential equations
• Global rates of convergence in log-concave density estimation
• Approximation by log-concave distributions, with applications to regression
• Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency
• Deciding polynomial-transcendental problems
• Triangulations. Structures for algorithms and applications
• Probability density estimation using delta sequences
• Recent progress in log-concave density estimation
• Geometry of log-concave density estimation
• Adaptation in log-concave density estimation
• Maximum likelihood estimation of smooth monotone and unimodal densities.
• Estimation of a convex function: Characterizations and asymptotic theory.
• Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
• Fast multivariate log-concave density estimation
• Numerical algebraic geometry
• Estimation of a \(k\)-monotone density: limit distribution theory and the spline connection
• Log-concave probability and its applications
• Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental
• Nonparametric Estimation under Shape Constraints
• Algorithm 921
• Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties
• An Empirical Distribution Function for Sampling with Incomplete Information
• Remarks on Some Nonparametric Estimates of a Density Function
• Complexity of Bezout's Theorem I: Geometric Aspects
• Detecting the Presence of Mixing with Multiscale Maximum Likelihood
• Maximum Likelihood Estimation of a Multi-Dimensional Log-Concave Density
• On Recurrent Reachability for Continuous Linear Dynamical Systems
• Multivariate Density Estimation
• Fleshing out the generalized Lambert W function
• On the generalization of the Lambert $W$ function
• Computing maximum likelihood estimators of a log-concave density function
• On Estimation of a Probability Density Function and Mode
• Introduction to nonparametric estimation
• Maximum penalized likelihood estimation. Vol. 1: Density estimation