The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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?
In the citing paper
“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]
Citations
Cites
On Estimation of a Probability Density Function and Mode
Parzen, E. (1962) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177704472 · Cited by 10,831
An Algorithm for Finding Best Matches in Logarithmic Expected Time
Friedman, J. H., Bentley, J. L., & Finkel, R. A. (1977) · ACM Transactions on Mathematical Software · doi:10.1145/355744.355745 · Cited by 2,802
A Nonparametric Estimate of a Multivariate Density Function
Loftsgaarden, D. O., & Quesenberry, C. P. (1965) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177700079 · Cited by 800
Nonparametric probability density estimation
Tapia, R. A., & Thompson, J. (1978) · Cited by 454
Characterization of cyclostationary random signal processes
Gardner, W. A., & Franks, L. (1975) · IEEE Transactions on Information Theory · doi:10.1109/tit.1975.1055338 · Cited by 424
Patterns in pattern recognition: 1968-1974
Kanal, L. N. (1974) · IEEE Transactions on Information Theory · doi:10.1109/tit.1974.1055306 · Cited by 282
Nonparametric Probability Density Estimation: I. A Summary of Available Methods
Wegman, E. J. (1972) · Technometrics · doi:10.1080/00401706.1972.10488943 · Cited by 237
Frontiers of Pattern Recognition
(1972) · Elsevier eBooks · doi:10.1016/c2013-0-11670-4 · Cited by 237
Nonparametric estimates of probability densities
Wagner, T. J. (1975) · IEEE Transactions on Information Theory · doi:10.1109/tit.1975.1055408 · Cited by 65
A HIERARCHY OF PROBABILITY DENSITY FUNCTION ESTIMATES
Cover, T. M. (1972) · Elsevier eBooks · doi:10.1016/b978-0-12-737140-5.50010-5 · Cited by 20
Research works printed but not linked: 2
- Breiman L., 1975, J. Amer. Statist. Assoc.
- Meisel, W. “The Complete Pattern Recognition Algorithm”. 8th Annual Symposium on the Interface Between Computer Science and Statistics, Health Sciences Computing Facility, UCLA.
Cited by
Sorted by citations
Items 401–489 of 489
Interpolative response modeling for Monte Carlo simulation
Campbell, L., & Purviance, J. E. (2002) · IEEE MTT-S International Microwave Symposium digest · doi:10.1109/mwsym.1994.335417
Credibility Using Semiparametric Models With Adaptive Kernel
Demir, S., & Mert, M. (2013) · DergiPark (Istanbul University)
On convergence of kernel estimators of density with variable window width by dependent observations
Dobrovidov, A. V. (2007) · Automation and Remote Control · doi:10.1134/s0005117907090123
A Note on the Variable Kernel Estimate
Schäfer, H., & Trampisch, H. J. (1982) · Biometrical Journal · doi:10.1002/bimj.4710240609
Constrained optimal neighborhoods and kernel estimators as improvements to applications of kriging.
Moody, M. M. (1993) · UA Campus Repository (The University of Arizona)
Model‐free data screening and cleaning
Tarter, M. E. (2011) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.140
Optimal Quantile Principle for Selecting Variable Bandwidth in Regression Estimators
Kozek, A. S., & Schuster, E. F. (1992) · Springer eBooks · doi:10.1007/978-1-4612-2856-1_63
Ultimate performance of QEM classifiers
Comon, P., & Bienvenu, G. (1996) · IEEE Transactions on Neural Networks · doi:10.1109/72.548185
Sparse Mixture Conditional Density Estimation by Superficial Regularization
Krauthausen, P., Ruoff, P., & Hanebeck, U. D. (2011) · Repository KITopen (Karlsruhe Institute of Technology) · doi:10.5445/ir/1000035129
Multiparameter Kernel Estimates
Devroye, L., & Lugosi, G. (2001) · Springer series in statistics · doi:10.1007/978-1-4613-0125-7_12
Bowles, D. S., Bingham, G. E., Lall, U., Tarboton, D. G., Al-Adhami, M., Jensen, D. T., & McCurdy, G. D. (1990) · Digital Commons - USU (Utah State University)
Comparing nonparametric density estimators using different canonical kernel functions
Yousif, M., & Rasheed, D. H. (2010) · IRAQI JOURNAL OF STATISTICAL SCIENCES · doi:10.33899/iqjoss.2010.030478
Bayesian sampling for smoothing parameter estimation
Hu, S. (2017) · Figshare · doi:10.4225/03/58b3b566192ce
Data-guided statistical sparse measurements modeling for compressive sensing
Schwartz, T. (2013) · UWSpace (University of Waterloo)
Bias Correction for Regularized Regression and its Application in Learning with Streaming DataPreprint
Wu, Q. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.04882
Order statistics and nearest neighbors
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_1
Regression: the noiseless case
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_15
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_17
Covariance approximation of nonlinear regression
Витальевич, Л. Л., Лабунец, Е. Л., & Lebedeva, N. L. (2016) · Journal of Communications Technology and Electronics · doi:10.1134/s106422691607007x
The nearest neighbor rule: variable k
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_19
Framework for local polynomial regression
B, J. F. A., & Gijbels, I. (2018) · Routledge eBooks · doi:10.1201/9780203748725-3
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_14
Advanced properties of uniform order statistics
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_13
The choice of a nearest neighbor estimate
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_16
L p -consistency and Stone’s theorem
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_10
The nearest neighbor rule: fixed k
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_18
The k-nearest neighbor density estimate
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_3
Density estimation communication systems
Wang, P. (2007) · doi:10.32657/10356/3472
Online Variable Kernel Estimator
Lakhdar, Y., & Sbai, E. H. (2016) · International Journal of Operations Research and Information Systems · doi:10.4018/ijoris.2017010104
FROG: A Fast and Reliable Crowdsourcing Framework (Technical Report)Preprint
Cheng, P., Lian, X., Jian, X., & Chen, L. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1610.08411
Splines, Smoothers, and Kernels
Berk, R. A. (2016) · Springer texts in statistics · doi:10.1007/978-3-319-44048-4_2
Probability density estimation using two new kernel functions
Rodchuen, M., & Suwattee, P. (2010)
Annotating Geographical Objects in OpenStreetMap with Geo-tagged Social Media
Chen, X., Vo, H., & Wang, F. (2016) · doi:10.1145/3021304.3021306
Performance of Bandwidth Selection Rules for the Local Linear RegressionPreprint
Hill, R. C., & Lee, K.-S. (2001) · RePEc: Research Papers in Economics
Semi-supervised Bayesian classification by vector features with continuous and discrete components
Vasilyev, V., & Dobrovidov, A. V. (2017) · International Conference on Information and Digital Technologies (IDT) · doi:10.1109/dt.2017.8024328
Semi-parametric density estimation
Stride, C. (2026) · Warwick Research Archive Portal (University of Warwick) · doi:10.82444/warw.33767116
MacDonald, Z., & Pudney, S. E. (2018) · Routledge eBooks · doi:10.4324/9781315185194-8
Nonparametric PU Learning of State Estimation in Markov Switching Model
Dobrovidov, A. V., & Vasilyev, V. (2018) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-96941-1_2
Machine Learning Techniques as Applied to Discrete and Combinatorial Structures
Schwartz, S. D. (2019) · Digital Commons - USU (Utah State University) · doi:10.26076/2qjd-w239
Personalized Check-in Prediction Model Based on User’s Dissimilarity and Regression
Su, C., Zhou, Q., Xie, X., & Wu, D. (2019) · IEEE Access · doi:10.1109/access.2019.2923435
Efficient and flexible Bayesian synthetic likelihood via transformations
Priddle, J. W. (2020) · Queensland University of Technology · doi:10.5204/thesis.eprints.205902
Refined Mode-Clustering via the Gradient of Slope
Zhang, K., & Chen, Y. (2021) · Stats · doi:10.3390/stats4020030
Seber, G. A. F. (1984) · Wiley series in probability and statistics · doi:10.1002/9780470316641.refs
Nonparametric Models and Bayesian Networks. Applications to Anomaly Detection
González, D. A. (2021) · doi:10.20868/upm.thesis.69348 · Cited by 1
Tuning selection for two-scale kernel density estimators
Yu, X., Wang, C., Yang, Z., & Jiang, B. (2022) · Computational Statistics · doi:10.1007/s00180-022-01196-6
Full Rotation Hyper-ellipsoid Multivariate Adaptive Bandwidth Kernel Density Estimator
van Zyl, T. L. (2022) · Communications in computer and information science · doi:10.1007/978-3-030-95070-5_19
Nearest‐Neighbor Density Estimation
Yu, J. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0692
The 1-nearest neighbor regression function estimate
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_9
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_7
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_12
(2011) · Wiley eBooks · doi:10.1002/9781119952954.refs
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_6
Givens, G. H., & Hoeting, J. A. (2012) · Computational Statistics · doi:10.1002/9781118555552.refs
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_4
Scott, D. W. (2015) · Wiley series in probability and statistics · doi:10.1002/9781118575574.bref
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_20
Gérard Biau, A., & Devroye, L. (2015) · Springer series in the data sciences · doi:10.1007/978-3-319-25388-6_11
Scott, D. W. (1992) · Wiley series in probability and statistics · doi:10.1002/9780470316849.refs
Tessellation-based Kernel Density Estimation
Belov, V., & Mařík, R. (2021) · International Conference on Algorithms, Computing and Artificial Intelligence (ACAI) · doi:10.1145/3508546.3508582
(1983) · Elsevier eBooks · doi:10.1016/b978-0-12-564020-6.50017-7
Framework for local polynomial regression
B, J. F. A., & Gijbels, I. (1994) · Springer eBooks · doi:10.1007/978-1-4899-3150-4_3
La cointégration non linéaire : une note méthodologique
Dufrénot, G., & Mignon, V. (2002) · Économie & prévision · doi:10.3917/ecop.155.0117
Dasgupta, A. (2008) · Springer eBooks · doi:10.1007/978-0-387-75971-5_32
Discussion of the Paper by Dr Diggle and Dr Gratton
(1984) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1984.tb01291.x
Splines, Smoothers, and Kernels
Berk, R. A. (2020) · Springer texts in statistics · doi:10.1007/978-3-030-40189-4_2
Nearest‐Neighbor Density Estimation
Yu, J. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0692.pub2
Methodology for nonparametric bias reduction in kernel regression estimation
Slaoui, Y. (2023) · Monte Carlo Methods and Applications · doi:10.1515/mcma-2022-2130
(2023) · Geoscientific model development · doi:10.5194/gmd-2023-17-rc1
(2023) · Geoscientific model development · doi:10.5194/gmd-2023-17-rc2
Pelz, M.-T. (2023) · Geoscientific model development · doi:10.5194/gmd-2023-17-ac1
Tang, B., & Li, X. (2024) · Springer optimization and its applications · doi:10.1007/978-3-031-58923-2_2
An Improved Bayesian Learner based on Weighted Beta Kernel Density Estimation
Liu, Y., Ye, Z., Bai, W., Кочан, О. В., Zhang, Y., & Xu, D. (2024) · International Conference on Advanced Computer Information Technologies (ACIT) · doi:10.1109/acit62333.2024.10712457
Multiscale local polynomial density estimation
Jansen, M. (2024) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2024.2434933
Modified nonparametric spectral density estimation under long-range dependence
Kim, Y. M. (2025) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2025.2542542
Plastics as vectors of radiocesium in river environments of Fukushima, Japan
Battulga, B., Nakanishi, T., Ikenoue, T., Atarashi-Andoh, M., & Koarashi, J. (2025) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2025.140593
Berile, N. K., Bezabeh, M. A., & Bekele, S. A. (2025) · Structural Safety · doi:10.1016/j.strusafe.2025.102671
circularKDE: Recent Methods for Kernel Density Estimation of Circular Data
Zámečník, S., Hórová, I., Hasilová, K., & Katina, S. (2026) · doi:10.32614/cran.package.circularkde
Cobbs, K. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.5975594
SARS-CoV-2 membrane protein conformations induce distinct membrane curvaturesPreprint
McTiernan, J., Zandi, R., Colvin, M. E., & Ajay Gopinathan, A. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.07.06.736641
An FPGA based readout system for sub-nanosecond beam background characterization
Eisele, F., Hummer, F., Scomparin, L., Khechen, D. E., Steinmann, J. L., Noll, M., Vollmer, Y., & Simon, F. (2026) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/j.nima.2026.172014
Kernel-Density Mismatch in Drifting Models: Rank-Anchored Calibration for One-Step GenerationPreprint
Wang, Z., Liu, J., Zhao, Z., & Dong, X. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7412572
Data Driven Bandwidth for Medoid Shift Algorithm
Gilani, S. Z., & Rao, N. I. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-21887-3_41
Metadata
- 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
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