Kernel density estimation via diffusion
Open accessAbstract
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.
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The heat kernel uses diffusion to adapt locally in regions of varying data density, as seen in single-cell data.
“This kernel uses diffusion to provide local adaptivity in regions of varying data density21, such as is observed in single-cell data.”
From Quantifying the effect of experimental perturbations at single-cell resolution (2021) · cites this paper as [21]
The number of mRNA molecules may sometimes not correlate well with the numbers of their protein products at the same time point.
“Third, the number of mRNA molecules may sometimes not correlate well with the numbers of their protein products at the same time point180–184”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [183]
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- Authors
- Botev, Z. I., Grotowski, J. F., & Kroese, D. P.
- Affiliations
- The University of Queensland (AU)
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2010-10-01
- Volume
- 38
- Issue
- 5
- Pages
- 2916-2957
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- OpenAlex
- W2153464267
- Cited by
- 1,689
- References
- 41
- Citations by year
- 2026: 70 · 2025: 121 · 2024: 118 · 2023: 111 · 2022: 146 · 2021: 145 · 2020: 142 · 2019: 141 · 2018: 139 · 2017: 110 · 2016: 92 · 2015: 75 · 2014: 81 · 2013: 97 · 2012: 57
- FWCI
- 53.33
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- kernel density estimation, adaptive smoothing, bandwidth selection, nonparametric density estimation
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