Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach

Polonik, Wolfgang

doi:10.1214/aos/1176324626

Cited by 218 publications

(239 citation statements)

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“…Further work in the context of investigating multimodality is provided by Müller and Sawitzki (1991) using their concept of excess mass. Their ideas have been extended to multidimensional distributions by Polonik (1995aPolonik ( , 1995bPolonik ( , 1999. Minotte and Scott (1993) consider mode trees where they calculate the modes of a kernel estimator for a scale of bandwidths and then plot the locations of the modes against the bandwidths.…”

Section: Previous Workmentioning

confidence: 99%

Bivariate density estimation using BV regularisation

Obereder

Scherzer

Kovac

2007

Computational Statistics & Data Analysis

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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 taut-string 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.

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Section: Previous Workmentioning

confidence: 99%

Bivariate density estimation using BV regularisation

Obereder

Scherzer

Kovac

2007

Computational Statistics & Data Analysis

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“…One can cite the works of Cadre [1], Cuevas and Fraiman [2], Hartigan [3], Polonik [4], Tsybakov [5], Walther [6]. This large number of works on this subject is motivated by the high number of possible applications.…”

Section: Introductionmentioning

confidence: 99%

“…This large number of works on this subject is motivated by the high number of possible applications. Estimating these level sets can be useful in mode estimation (Müller and Stawitzki [7], Polonik [4]), or in clustering (Biau, Cadre and Pelletier [8], Cuevas, Febrero and Fraiman [9,10]). In particular, Biau, Cadre and Pelletier [8] use an estimator of the level sets of the density function to determine the number of clusters.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation of regression level sets using kernel plug-in estimator

Laloë¹,

Servien

2013

Journal of the Korean Statistical Society

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“…Contributions include Hartigan (1987), Müller & Sawitzki (1991), Polonik (1995), Tsybakov (1997), Baíllo, Cuesta-Albertos & Cuevas (2001), Cadre (2006) and Jang (2006). Alternative terminology includes estimation of the density contours, density level sets and excess mass regions.…”

Section: Introductionmentioning

confidence: 99%

Highest Density Difference Region Estimation with Application to Flow Cytometric Data

Duong¹,

Koch²,

Wand³

2009

Biometrical J

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Motivated by the needs of scientists using flow cytometry, we study the problem of estimating the region where two multivariate samples differ in density. We call this problem highest density difference region estimation and recognise it as a two-sample analogue of highest density region or excess set estimation. Flow cytometry samples are typically in the order of 10,000 and 100,000 and with dimension ranging from about 3 to 20. The industry standard for the problem being studied is called Frequency Difference Gating, due to Roederer & Hardy (2001). After couching the problem in a formal statistical framework we devise an alternative estimator that draws upon recent statistical developments such as patient rule induction methods (PRIM). Improved performance is illustrated in simulations. While motivated by flow cytometry, the methodology is suitable for general multivariate random samples where density difference regions are of interest.

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Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach

Cited by 218 publications

References 0 publications

Bivariate density estimation using BV regularisation

Bivariate density estimation using BV regularisation

Nonparametric estimation of regression level sets using kernel plug-in estimator

Highest Density Difference Region Estimation with Application to Flow Cytometric Data

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