Corpus ID: 212644482

Exact Solutions in Log-Concave Maximum Likelihood Estimation

@article{Grosdos2020ExactSI,
  title={Exact Solutions in Log-Concave Maximum Likelihood Estimation},
  author={Alexandros Grosdos and Alexander Heaton and Kaie Kubjas and Ol'ga V. Kuznetsova and Georgy Scholten and Miruna-Stefana Sorea},
  journal={arXiv: Statistics Theory},
  year={2020}
}
  • Alexandros Grosdos, Alexander Heaton, +3 authors Miruna-Stefana Sorea
  • Published 2020
  • Mathematics
  • arXiv: Statistics Theory
  • We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many quantities, namely the function values, or heights, at the data points. We explore in what sense exact solutions to this problem are possible. First, we show that the heights given by the maximum likelihood estimate are generically transcendental. For a cell… CONTINUE READING

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