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Asymptotics and optimal bandwidth selection for highest density region estimation
 Annals of Statistics
"... We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, we derive a uniforminbandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimat ..."
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Cited by 11 (1 self)
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We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, we derive a uniforminbandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.
Bivariate density estimation using BV regularisation
, 2007
"... The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the tautstring algorithm which provides adequate approxi ..."
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Cited by 7 (0 self)
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The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the tautstring algorithm which provides adequate approximations with a small number of local extrema is generalised for analysing two and higher dimensional data, using Delaunay triangulation and diffusion filtering. Results are based on equivalence relations in one dimension between the taut string algorithm and the method of solving the discrete total variation flow equation. The generalisation and some modifications are developed and the performance for density estimation is shown.
Cluster Analysis of Massive Datasets in Astronomy
, 2006
"... Clusters of galaxies are a useful proxy to trace the mass distribution of the universe. By measuring the mass of clusters of galaxies at different scales, one can follow the evolution of the mass distribution (Martínez and Saar, 2002). It can be shown that finding galaxies clustering is equivalent t ..."
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Cited by 6 (0 self)
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Clusters of galaxies are a useful proxy to trace the mass distribution of the universe. By measuring the mass of clusters of galaxies at different scales, one can follow the evolution of the mass distribution (Martínez and Saar, 2002). It can be shown that finding galaxies clustering is equivalent to finding density contour clusters (Hartigan, 1975): connected components of the level set Sc ≡ {f> c} where f is a probability density function. Cuevas et al. (2000, 2001) proposed a nonparametric method for density contour clusters. They attempt to find density contour clusters by the minimal spanning tree. While their algorithm is conceptually simple, it requires intensive computations for large datasets. We propose a more efficient clustering method based on their algorithm with the Fast Fourier Transform (FFT). The method is applied to a study of galaxy clustering on large astronomical sky survey data.
A Fast Clustering Algorithm with Application to Cosmology
, 2004
"... We present a fast clustering algorithm for density contour clusters (Hartigan, 1975) that is a modified version of the Cuevas, Febrero and Fraiman (2000) algorithm. By Hartigan’s definition, clusters are the connected components of a level set Sc ≡ {f> c} where f is the probability density functi ..."
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Cited by 2 (2 self)
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We present a fast clustering algorithm for density contour clusters (Hartigan, 1975) that is a modified version of the Cuevas, Febrero and Fraiman (2000) algorithm. By Hartigan’s definition, clusters are the connected components of a level set Sc ≡ {f> c} where f is the probability density function. We use kernel density estimators and orthogonal series estimators to estimate f and modify the Cuevas, Febrero and Fraiman (2000) Algorithm to extract the connected components from level set estimators ̂ Sc ≡ { ̂ f> c}. Unlike the original algorithm, our method does not require an extra smoothing parameter and can use the Fast Fourier Transform (FFT) to speed up the calculations. We show the cosmological definition of clusters of galaxies is equivalent to density contour clusters and present an application in cosmology. Key Words: Density contour cluster; clustering; Fast Fourier Transform. 1
Confidence Regions for Level Sets
, 2012
"... This paper discusses a universal approach to the construction of confidence regions for level sets {h(x) ≥ 0} ⊂Rd of a function h of interest. The proposed construction is based on a plugin estimate of the level sets using an appropriate estimate hn of h. The approach provides finite sample upper ..."
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This paper discusses a universal approach to the construction of confidence regions for level sets {h(x) ≥ 0} ⊂Rd of a function h of interest. The proposed construction is based on a plugin estimate of the level sets using an appropriate estimate hn of h. The approach provides finite sample upper and lower confidence limits. This leads to generic conditions under which the constructed confidence regions achieve a prescribed coverage level asymptotically. The construction requires an estimate of quantiles of the distribution of sup∆n hn(x) − h(x)  for appropriate sets ∆n ⊂ R d. In contrast to related work from the literature, the existence of a weak limit for an appropriately normalized process {hn(x),x ∈ D} is not required. This adds significantly to the challenge of deriving asymptotic results for the corresponding coverage level. Our approach is exemplified in the case of a density level set utilizing a kernel density estimator and a bootstrap procedure.
ASYMPTOTICS AND OPTIMAL BANDWIDTH SELECTION FOR
, 2009
"... We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, we derive a uniforminbandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimat ..."
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We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, we derive a uniforminbandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.
METHODOLOGY ARTICLE Open Access Misty Mountain clustering: application to fast
"... unsupervised flow cytometry gating ..."
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proposal to offer a Graduate Certificate in Latin American and Caribbean
, 2010
"... (The Bylaws prohibit representation by proxy.) ..."
Centre for Statistical and Survey Methodology
, 2008
"... Highest density difference region estimation with application to flow cytometric data ..."
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Highest density difference region estimation with application to flow cytometric data