The DOI matches its Crossref record.
On Estimation of a Probability Density Function and Mode
Open accessAbstract
Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and of determining the mode of a probability function are discussed. Only estimates which are consistent and asymptotically normal are constructed. (Author)
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Chandola, V., Banerjee, A., & Kumar, V. (2009) · ACM Computing Surveys · doi:10.1145/1541880.1541882 · Cited by 11,687
Nadaraya, E. A. (1964) · Theory of Probability & Its Applications · doi:10.1137/1109020 · Cited by 3,462
A review of classification algorithms for EEG-based brain–computer interfaces: A 10 year update
Lotte, F., Bougrain, L., Cichocki, A., Clerc, M., Congedo, M., Rakotomamonjy, A., & Yger, F. (2018) · Journal of Neural Engineering · doi:10.1088/1741-2552/aab2f2 · Cited by 2,239
Gong, D., Liu, L., Le, V., Saha, B., Mansour, M. R., Venkatesh, S., & Van Den Hengel, A. (2019) · 2019 IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00179 · Cited by 1,930
Recovering Gene Interactions from Single-Cell Data Using Data Diffusion
van Dijk, D., Sharma, R., Nainys, J., Yim, K., Kathail, P., Carr, A. J., Burdziak, C., Moon, K. R., Chaffer, C. L., Pattabiraman, D., et al. (2018) · Cell · doi:10.1016/j.cell.2018.05.061 · Cited by 1,829
Metadata
- Authors
- Parzen, E.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1962-09
- Volume
- 33
- Issue
- 3
- Pages
- 1065-1076
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2118020555
- Cited by
- 10,585
- References
- 0
- FWCI
- 10.47
- Type
- journal article
- Language
- en
- Open access
- bronze
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On Estimation of a Probability Density Function and Mode. https://app.cochat.ai/papers/10.1214/aoms/1177704472
- The paper
- Parzen, E. (1962). On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177704472
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.