Title: Exact solutions in log-concave maximum likelihood estimation
Authors: Alexandros Grosdos - Osnabrück University (Germany)
Kaie Kubjas - Aalto University (Finland) [presenting]
Olga Kuznetsova - Aalto University (Finland)
Georgy Scholten - North Carolina State University (United States)
Miruna-Stefana Sorea - MPI Leipzig (Germany)
Bernd Sturmfels - MPI Leipzig and University of California Berkeley (Germany)
Abstract: In nonparametric statistics one abandons the requirement that a probability density function belongs to a statistical model with finitely many parameters, and instead requires that it satisfies certain constraints. The logarithm of a probability density function is concave. The logarithm of the maximum likelihood estimate has been shown to be a piecewise linear function. We study exact solutions to log-concave maximum likelihood estimation in special cases.