Reference : Some simple variance bounds from Stein’s method
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Some simple variance bounds from Stein’s method
Ley, Christophe mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Daly, Fraser [Heriot-Watt University > Department of Actuarial Mathematics and Statistics]
Ghaderinezhad, Fatemeh [Ghent University > Department of Applied Mathematics, Computer Science and Statistics]
Swan, Yvik [Université Libre de Bruxelles - ULB > Department of Mathematics]
ALEA: Latin American Journal of Probability and Mathematical Statistics
Instituto Nacional de Matematica Pura e Aplicada
Yes (verified by ORBilu)
Rio de Janeiro
[en] Stein kernel ; Stein operator ; prior density ; stochastic ordering ; variance bound
[en] Using coupling techniques based on Stein’s method for probability approximation, we revisit
classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Our bounds are
immediate in any context wherein a Stein identity is available. After providing illustrative examples
for a Gaussian and a Gumbel target distribution, our main contributions are new variance bounds in settings where the underlying density function is unknown or intractable. Applications include bounds for analysis of the posterior in Bayesian statistics, bounds for asymptotically Gaussian random variables using zero-biased couplings, and bounds for random variables which are New Better (Worse) than Used in Expectation.

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