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Limit Theory in Probability
Rates of convergence and asymptotic expansions in the multivariate central limit theorem. The approach via convolution operators, rather than the more usual approach via characteristic functions, enabled known results to be improved and extended (Ann. Probability, 1977, 1980). In particular, Berry-Esseen-type bounds were shown to be valid for arbitrary Borel sets. Extreme value theory. In Ann. Probability (1985) identification of a certain slowly varying function provided the key to a number of characterisations which simplified and extended existing results in local limit theory. Suitable expansions of regularly varying functions lead to asymptotic expansions for extreme quantiles (Lecture Notes in Statist., 1989). Local and conditional limit theory more generally has been a topic of interest. Papers appeared in Ann. Statist. (1986) and J. Theoret. Prob. (1989).
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