18,843 research outputs found
フィリピンの小児入院患者およびペルーの出生コホートにおけるサポウイルスの有病率と遺伝学的多様性
Tohoku University押谷仁課
Edgeworth Expansion by Stein's Method
Edgeworth expansion provides higher-order corrections to the normal
approximation for a probability distribution. The classical proof of Edgeworth
expansion is via characteristic functions. As a powerful method for
distributional approximations, Stein's method has also been used to prove
Edgeworth expansion results. However, these results assume that either the test
function is smooth (which excludes indicator functions of the half line) or
that the random variables are continuous (which excludes random variables
having only a continuous component). Thus, how to recover the classical
Edgeworth expansion result using Stein's method has remained an open problem.
In this paper, we develop Stein's method for two-term Edgeworth expansions in a
general case. Our approach involves repeated use of Stein equations, Stein
identities via Stein kernels, and a replacement argument.Comment: 22 page
On the Approximate Core and Nucleon of Flow Games
The flow game with public arcs is a cooperative revenue game derived from a
flow network. In this game, each player possesses an arc, while certain arcs,
known as public arcs, are not owned by any specific player and are accessible
to any coalition. The aim of this game is to maximize the flow that can be
routed in the network through strategic coalition formation. By exploring its
connection to the maximum partially disjoint path problem, we investigate the
approximate core and nucleon of the flow game with public arcs. The approximate
core is an extension of the core that allows for some deviation in group
rationality, while the nucleon is a multiplicative analogue of the nucleolus.
In this paper, we provide two complete characterizations for the optimal
approximate core and show that the nucleon can be computed in polynomial time
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