Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation

By Tarn Duong, Martin L. Hazelton. 2005

335 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/04886c50dc6f501fda529935f5e329674f4631c9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Giovanna Menardi
2. Jose Emmanuel Chacón
3. Medhi Bennis
4. Rob J Hyndman
5. Han Lin Shang
6. Walid Saad
7. Chu V. Mai
8. Bruno Sudret

In Statistics and Probability

1. Giovanna Menardi
2. Han Lin Shang
3. Jose Emmanuel Chacón
4. Rob J Hyndman
5. Walid Saad
6. Merouane Debbah
7. Bruno Sudret
8. Chu V. Mai

Citations in the corpus

• Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices (2010, methodology): “As in Duong and Hazelton (2005a), this rate may be defined to be n−α if vec(ĤPI − HAMISE) = OP (Jdn−α)vec HAMISE, where Jd denotes the d × d matrix of ones, and the OP notation is meant to be applied element-wise.”
• Beyond 5G With UAVs: Foundations of a 3D Wireless Cellular Network (2018, methodology): “We repeat this operation and take an average with L log-likelihood values, i.e., It can be shown [35], [36] that: and since we can find h x , h y , and h z by a cross-validation method as: Hence, we can say that −L ( h x , h y , h z ) is a biased estimator of MISE.”
• Rainbow Plots, Bagplots, and Boxplots for Functional Data (2010, methodology): “We select the bandwidths using smoothed cross validation (Duong & Hazelton 2005).”
• ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R (2007, background): “More extensive simulation studies are reported in Duong and Hazelton (2003, 2005b).”
• Seismic fragility curves for structures using non-parametric representations (2017, positive): “In this case, the smoothed cross-validation estimator is the most reliable among the cross-validation methods [42].”
• A Review on Modal Clustering (2016, methodology): “Consolidated methods for multivariate densities are based on plug-in (Wand & Jones, 1994; Duong & Hazelton, 2003; Chacón & Duong, 2010) or cross-validation rules (Sain et al., 1994; Duong & Hazelton, 2005).”