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Some simple variance bounds from Stein's method

Tijdschriftbijdrage - Tijdschriftartikel

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 illus-trative 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. Appli-cations 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.
Tijdschrift: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS
ISSN: 1980-0436
Issue: 2
Volume: 18
Pagina's: 1845 - 1858
Jaar van publicatie:2021
Toegankelijkheid:Open