Displaying similar documents to “On normal approximation of large products of functions: A refinement of Blackwell's result.”

Diophantine approximation and special Liouville numbers

Johannes Schleischitz (2013)

Communications in Mathematics

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This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers ζ 1 , ζ 2 , ... , ζ k . The approach relies on results on the connection between the set of all s -adic expansions ( s ≥ 2 ) of ζ 1 , ζ 2 , ... , ζ k and their associated approximation constants. As an application, explicit construction of real numbers ζ 1 , ζ 2 , ... , ζ k with prescribed approximation properties are deduced and illustrated by Matlab plots.

Asymptotic distributions οf linear combinations of order statistics

Małgorzata Bogdan (1994)

Applicationes Mathematicae

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We study the asymptotic distributions of linear combinations of order statistics (L-statistics) which can be expressed as differentiable statistical functionals and we obtain Berry-Esseen type bounds and the Edgeworth series for the distribution functions of L-statistics. We also analyze certain saddlepoint approximations for the distribution functions of L-statistics.