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Analysis of the quality of approximations in the statistical analysis of multivariate observations
Fördergeber - Sonstige;
Second-order Chebyshev-Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse exponential distributions. A formal construction of asymptotic expansions is developed. Therefore, the results can be applied to a whole family of asymptotically normal or chi-square statistics. The first Chebyshev-Edgeworth expansions for asymptotic chi-square statistics based on random sample sizes were proved. The statistics allow non-random, random, and mixed normalization factors.

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