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http://hdl.handle.net/1942/27696
Title: | Approximate Central Limit Theorems | Authors: | BERCKMOES, Ben MOLENBERGHS, Geert |
Issue Date: | 2018 | Publisher: | SPRINGER/PLENUM PUBLISHERS | Source: | JOURNAL OF THEORETICAL PROBABILITY, 31(3), p. 1590-1605 | Abstract: | We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg's condition. This allows us to continue to provide information in nonstandard settings in which the classical central limit theorem fails to hold. Stein's method plays a key role in the development of this theory. | Notes: | [Berckmoes, Ben] Univ Antwerp, Antwerp, Belgium. [Molenberghs, Geert] Univ Hasselt, Hasselt, Belgium. [Molenberghs, Geert] Katholieke Univ Leuven, Leuven, Belgium. | Keywords: | Kolmogorov metric; Lindeberg-Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein's method; Wasserstein metric;Kolmogorov metric; Lindeberg–Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein’s method; Wasserstein metric | Document URI: | http://hdl.handle.net/1942/27696 | ISSN: | 0894-9840 | e-ISSN: | 1572-9230 | DOI: | 10.1007/s10959-017-0744-6 | ISI #: | 000441304800012 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
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berckmoes 1.pdf Restricted Access | Published version | 456.33 kB | Adobe PDF | View/Open Request a copy |
506.pdf | Peer-reviewed author version | 3.09 MB | Adobe PDF | View/Open |
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