Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Nile Problem by Sir Ronald Fisher   The Nile problem by Ronald Fisher may be interpreted as the problem of making
statistical inference for a special curved exponential family when the minimal
sufficient statistic is incomplete. The problem itself and its versions for
general curved exponential families pose a mathematical-statistical challenge:
studying the subalgebras of ancillary statistics within the $\sigma$-algebra of
the (incomplete) minimal sufficient statistics and closely related questions of
the structure of UMVUEs.
  In this paper a new method is developed that, in particular, proves that in
the classical Nile problem no statistic subject to mild natural conditions is a
UMVUE. The method almost solves an old problem of the existence of UMVUEs. The
method is purely statistical (vs. analytical) and works for any family
possessing an ancillary statistic. It complements an analytical method that
uses only the first order ancillarity (and thus works when the existence of
ancillary subalgebras is an open problem) and works for curved exponential
families with polynomial constraints on the canonical parameters of which the
Nile problem is a special case.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph