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Stein-type covariance identities: Klaassen, Papathanasiou and Olkin-Shepp type bounds for arbitrary target distributions

Abstract:

In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wide family of Stein-Covariance identities which we put to use for revisiting the very classical topic of bounding the variance of functionals of random variables. Applying the Cauchy-Schwarz inequality yields first order upper and lower Klaassen-type variance bounds. A probabilistic representation of Lagrange's ident...

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Publication status:
Not Published
Peer review status:
Not peer reviewed
Version:
Author's Original

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Publication date:
2018-12-21
Pubs id:
pubs:955253
URN:
uri:80beee6f-931e-41c6-b8a5-cdb0c64a3a3f
UUID:
uuid:80beee6f-931e-41c6-b8a5-cdb0c64a3a3f
Local pid:
pubs:955253

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