Cited by 678Probability and Statistical ResearchStatistical Methods and InferenceStatistical Methods and Applications

Elements of Large-Sample Theory

Erich L. Lehmann·1999·Springer Texts in Statistics

Integrity signals

Registry

Crossref · 10.1007/b98855

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • 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]

Cites

Still being checked.

Cited by

Sorted by citations

Authors
Lehmann, E. L.
Affiliations
University of California, Berkeley (US)
Corresponding author
Erich L. Lehmann
Venue
Springer Texts in Statistics
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
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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review