# Approximation via bounds for density ratios

Jon Wellner, University of Washington
Monday, November 18, 2019 - 2:30pm to 3:20pm
LOW 101
New error bounds for the approximation of distributions will be introduced. The approximation error will be quantified by the maximal density ratio of the distribution \$Q\$  to be approximated and its proxy \$P\$.  This non-symmetric measure implies bounds for the total variation distance between \$Q\$ and \$P\$, and can be more informative.

New explicit bounds will be given for two problems in particular:
(1)  Approximation of hypergeometric distributions by binomial distributions;
(2)  Approximation of generalized binomial distributions by Poisson distributions.
In the first case the resulting bounds for the total variation distance improve on the best known classical bounds obtained by Stein's method. In the second case our new bounds are nearly on a par with the bounds obtained by Chen (1975).
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