Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonparametric estimations and the diffeological Fisher metric   In this paper, first, we survey the concept of diffeological Fisher metric
and its naturality, using functorial language of probability morphisms, and
slightly extending L\^e'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.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin