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2023•Unpublished venueOpen access

On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem

Vitaly Sobolev, Sergey M. Ramodanov

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Abstract

We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions.

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We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions.

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Available abstract

We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions.

Key concepts: Remainder, Central limit theorem, Limit (mathematics), Asymptotic expansion, Term (time), Mathematics, Asymptotic analysis, Method of matched asymptotic expansions

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