Plug-in bandwidth matrices for bivariate kernel density estimation

By Tarn Duong, Martin L. Hazelton. 2003

341 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b25a80684c2bdfb349ace593e39450dc5c04cdbe

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In Artificial Intelligence

In Environmental Engineering

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Citations in the corpus

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation (2009, background): “Wand and Jones (1994) and Duong and Hazelton (2003) presented plug-in algorithms for choosing bandwidths for bivariate data.”
Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernal density estimation (2005, methodology): “From Duong and Hazelton [1], the SAMSE pilot bandwidth is g4;SAMSE 1⁄4 Oðn 1=ðdþ6ÞÞ: Straightforward calculations then give Bias $ crðgj;SAMSEÞ 1⁄4 Oðg2j;SAMSEÞ 1⁄4 Oðn 2=ðdþ6ÞÞ when it follows that E1⁄2DHðPI AMISEÞðHAMISEÞ 1⁄4 OðJd n ÞvechHAMISE: ð9Þ It can be shown that in the SAMSE plug-in method”
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).”
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).”
Probit Transformation for Nonparametric Kernel Estimation of the Copula Density (2014, methodology): “The bandwidth matrix H ST was selected via a direct plug-in method (Duong and Hazelton, 2003) in the transformed domain ( S, T ); · the improved probit-transformation estimators ˜ c ( τ, 1) and ˜ c ( τ, 2) , given by (2.10), based on a k -NN- type bandwidth matrix selected via cross-validation as…”
Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices (2010, methodology): “The relative rate obtained in the previous result is the same as for the SAMSE plug-in selector of Duong and Hazelton (2003) , which is slightly slower than the rate n −4/(d+12) attained by the full plug-in selector of Wand and Jones (1994).”
GetDist: a Python package for analysing Monte Carlo samples (2019, neutral): “[37] for a possible alternative solution) • With boundaries, the even ψ m 1 ,m 2 derivative terms can be approximated by imposing reflection boundary conditions (i.e. evaluating using DCT), but with m 1 or m 2 odd, ψ m 1 ,m 2 cannot be evaluated from the DCT transform (which assumes symmetry by…”
What Is the Proper Methodto Delineate Home Range of anAnimal Using Today’s AdvancedGPS Telemetry Systems: The Initial Step (2011, neutral): “…combined into the solve-the-equation plug-in method; Jones et al., 1996), appear to be an improved alternative because of better convergence and reasonable tradeoffs between bias and variance compared to first generation methods (Jones et al., 1996; Duong & Hazelton 2003, but see Loader 1999).”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, methodology): “…(Wand and Jones (1995), section 4.7), (iii) smoothed cross-validation (Hall et al., 1992; Duong, 2004), (iv) a two-stage plug-in rule (Duong and Hazelton, 2003), (v) Abramson’s method (this method, proposed in Abramson (1982), chooses a bandwidth matrix of the form hf̂ −1=2.x/A,…”
Traits Without Borders: Integrating Functional Diversity Across Scales. (2016, methodology): “Because these data are generally unavailable, TPDI values can be approximated using the measured traits and an estimated variability [47,60].”
Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation (2005, methodology): “However, imposing such a constraint on the bandwidth matrix can result in markedly suboptimal density estimates, even if the data are pre-sphered (Wand & Jones, 1993; Duong & Hazelton 2003).”
Exploring wind direction and SO2 concentration by circular–linear density estimation (2012, methodology): “A plug-in rule for selecting the bandwidth matrix B was proposed by Duong and Hazelton (2003). The reflected data sample in each square l = 1, .”
A human-machine adversarial scoring framework for urban perception assessment using street-view images (2019, methodology): “The case study included nine types of Gaode POIs, and used the mean integrated squared error (MISE) criterion (Duong and Hazelton 2003) to automatically determine the bandwidth of the Gaussian function-based kernel density analysis of POIs.”