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Under the stated assumptions, Lyapunov's condition is satisfied and Lyapunov's central mean theorem holds, so the sum of products of inputs and weights tends to a normal distribution for sufficiently large training samples.
“It can be shown [55] that under these assumptions, Lyapunov's condition is satisfied and that Lyapunov's central mean theorem holds; in this case the sum of products of inputs and weights will tend to a normal distribution given that the number of training samples is sufficiently large.”
From ModDrop: Adaptive Multi-Modal Gesture Recognition (2016) · cites this paper as [55]
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- Authors
- Lehmann, E. L.
- Affiliations
- University of California, Berkeley (US)
- Corresponding author
- Erich L. Lehmann
- Venue
- Springer Texts in Statistics
- Publisher
- Springer-Verlag
- Published
- 1999
- OpenAlex
- W4300699176
- Cited by
- 677
- References
- 0
- Citations by year
- 2026: 21 · 2025: 33 · 2024: 32 · 2023: 29 · 2022: 38 · 2021: 33 · 2020: 32 · 2019: 44 · 2018: 34 · 2017: 39 · 2016: 33 · 2015: 26 · 2014: 38 · 2013: 28 · 2012: 26
- FWCI
- 2.32
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- asymptotic theory, first-order asymptotics, density estimation, bootstrapping
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