Variable Kernel Estimates of Multivariate Densities
Abstract
A class of density estimates using a superposition of kernels where the kernel parameter can depend on the nearest neighbor distances is studied by the use of simulated data. Their performance using several measures of error is superior to that of the usual Parzen estimators. A tentative solution is given to the problem of calibrating the kernel peakedness when faced with a finite sample set.
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Asymmetric kernels such as the one in Equation 10 have a long tradition in kernel estimation; when a kernel estimator uses θ_K θ_Q, it is known as a balloon estimator, and papers such as Breiman et al. have used θ_Q as a function of x' (sample-adaptive smoothing).
“When a kernel estimator uses θ K θ Q , it is known as a balloon estimator [14].Papers such as Breiman et al. [10] have even used θ Q as a function of x ′ , known as sample-adaptive smoothing.”
From Learning to (Learn at Test Time): RNNs with Expressive Hidden States (2024) · cites this paper as Breiman et al. [10]
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- Authors
- Breiman, L., Meisel, W., & Purcell, E.
- Affiliations
- Technology Service Corporation (United States) (US)
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 1977-05
- Volume
- 19
- Issue
- 2
- Pages
- 135-144
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W2008572210
- Cited by
- 488
- References
- 10
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 8 · 2023: 18 · 2022: 11 · 2021: 17 · 2020: 10 · 2019: 14 · 2018: 13 · 2017: 13 · 2016: 13 · 2015: 30 · 2014: 13 · 2013: 14 · 2012: 16
- FWCI
- 3.51
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Technometrics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- multivariate density estimation, nearest neighbor distance, finite-sample estimation
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