Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating the reciprocal of a binomial proportion   As a classic parameter from the binomial distribution, the binomial
proportion has been well studied in the literature owing to its wide range of
applications. In contrast, the reciprocal of the binomial proportion, also
known as the inverse proportion, is often overlooked, even though it also plays
an important role in various fields including clinical studies and random
sampling. The maximum likelihood estimator of the inverse proportion suffers
from the zero-event problem, and to overcome it, alternative methods have been
developed in the literature. Nevertheless, there is little work addressing the
optimality of the existing estimators, as well as their practical performance
comparison. Inspired by this, we propose to further advance the literature by
developing an optimal estimator for the inverse proportion in a family of
shrinkage estimators. We further derive the explicit and approximate formulas
for the optimal shrinkage parameter under different settings. Simulation
studies show that the performance of our new estimator performs better than, or
as well as, the existing competitors in most practical settings. Finally, to
illustrate the usefulness of our new method, we also revisit a recent
meta-analysis on COVID-19 data for assessing the relative risks of physical
distancing on the infection of coronavirus, in which six out of seven studies
encounter the zero-event problem.

23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics