Bounding distributional errors via density ratios
Copyright policy )Bounding distributional errors via density ratios
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric measure is more informative than and implies bounds for the total variation distance. Explicit approximation problems include, among others, hypergeometric by binomial distributions, binomial by Poisson distributions, and beta by gamma distributions. In many cases we provide both upper and (matching) lower bounds.
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- Washington State University United States
- Statistical Laboratory University of Cambridge United Kingdom
- University of Bern Switzerland
- University of Bern Switzerland
- University of Mary United States
total variation distance, hypergeometric distribution, Mathematics - Statistics Theory, Statistics Theory (math.ST), relative errors, Approximations to statistical distributions (nonasymptotic), 4905 Statistics, 510 Mathematics, 49 Mathematical Sciences, FOS: Mathematics, 62E17, 60E05, 60E15, Poisson approximation, Convergence of probability measures, binomial distribution
total variation distance, hypergeometric distribution, Mathematics - Statistics Theory, Statistics Theory (math.ST), relative errors, Approximations to statistical distributions (nonasymptotic), 4905 Statistics, 510 Mathematics, 49 Mathematical Sciences, FOS: Mathematics, 62E17, 60E05, 60E15, Poisson approximation, Convergence of probability measures, binomial distribution
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