Nonparametric estimations and the diffeological Fisher metric

Abstract

In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending Lê's theory in \cite{Le2020} to include weakly $C^k$-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff--Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.

final version, 20 p.. version 1: 17 p. comments are welcome!

References in corpus (2)

• Probabilistic morphisms and Bayesian nonparametrics
• Diffeological statistical models, the Fisher metric and probabilistic mappings