Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Results for the Existence and Consistency of the MLE in the
  Bradley-Terry-Luce Model   Ranking problems based on pairwise comparisons, such as those arising in
online gaming, often involve a large pool of items to order. In these
situations, the gap in performance between any two items can be significant,
and the smallest and largest winning probabilities can be very close to zero or
one. Furthermore, each item may be compared only to a subset of all the items,
so that not all pairwise comparisons are observed. In this paper, we study the
performance of the Bradley-Terry-Luce model for ranking from pairwise
comparison data under more realistic settings than those considered in the
literature so far. In particular, we allow for near-degenerate winning
probabilities and arbitrary comparison designs. We obtain novel results about
the existence of the maximum likelihood estimator (MLE) and the corresponding
$\ell_2$ estimation error without the bounded winning probability assumption
commonly used in the literature and for arbitrary comparison graph topologies.
Central to our approach is the reliance on the Fisher information matrix to
express the dependence on the graph topologies and the impact of the values of
the winning probabilities on the estimation risk and on the conditions for the
existence of the MLE. Our bounds recover existing results as special cases but
are more broadly applicable.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex