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Cholaquidis A, Fraiman R, Moreno L. Universally consistent estimation of the reach. J Stat Plan Inference 2022. [DOI: 10.1016/j.jspi.2022.11.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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Spatial distribution of invasive species: an extent of occurrence approach. TEST-SPAIN 2022. [DOI: 10.1007/s11749-021-00783-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
AbstractEcological Risk Assessment faces the challenge of determining the impact of invasive species on biodiversity conservation. Although many statistical methods have emerged in recent years in order to model the evolution of the spatio-temporal distribution of invasive species, the notion of extent of occurrence, formally defined by the International Union for the Conservation of Nature, has not been properly handled. In this work, a novel and flexible reconstruction of the extent of occurrence from occurrence data will be established from nonparametric support estimation theory. Mathematically, given a random sample of points from some unknown distribution, we establish a new data-driven method for estimating its probability support S in general dimension. Under the mild geometric assumption that S is $$r-$$
r
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convex, the smallest $$r-$$
r
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convex set which contains the sample points is the natural estimator. A stochastic algorithm is proposed for determining an optimal estimate of r from the data under regularity conditions on the density function. The performance of this estimator is studied by reconstructing the extent of occurrence of an assemblage of invasive plant species in the Azores archipelago.
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Saavedra-Nieves P, Crujeiras RM. Nonparametric estimation of directional highest density regions. ADV DATA ANAL CLASSI 2021. [DOI: 10.1007/s11634-021-00457-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
AbstractHighest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismology.
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Refined Mode-Clustering via the Gradient of Slope. STATS 2021. [DOI: 10.3390/stats4020030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we propose a new clustering method inspired by mode-clustering that not only finds clusters, but also assigns each cluster with an attribute label. Clusters obtained from our method show connectivity of the underlying distribution. We also design a local two-sample test based on the clustering result that has more power than a conventional method. We apply our method to the Astronomy and GvHD data and show that our method finds meaningful clusters. We also derive the statistical and computational theory of our method.
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Affiliation(s)
- Wanli Qiao
- Department of Statistics, George Mason University, Fairfax, VA 22030, USA
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Aaron C. Convergence rate for the $\lambda $-Medial-Axis estimation under regularity conditions. Electron J Stat 2019. [DOI: 10.1214/19-ejs1581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Qiao W, Polonik W. Extrema of rescaled locally stationary Gaussian fields on manifolds. BERNOULLI 2018. [DOI: 10.3150/16-bej913] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Chen YC, Genovese CR, Wasserman L. Statistical inference using the Morse-Smale complex. Electron J Stat 2017. [DOI: 10.1214/17-ejs1271] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Aaron C, Cholaquidis A, Cuevas A. Detection of low dimensionality and data denoising via set estimation techniques. Electron J Stat 2017. [DOI: 10.1214/17-ejs1370] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Rodríguez-Casal A, Saavedra-Nieves P. A fully data-driven method for estimating the shape of a point cloud. ESAIM-PROBAB STAT 2016. [DOI: 10.1051/ps/2016015] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Pulkkinen S. Ridge-based method for finding curvilinear structures from noisy data. Comput Stat Data Anal 2015. [DOI: 10.1016/j.csda.2014.08.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Cuevas A, Llop P, Pateiro-López B. On the estimation of the medial axis and inner parallel body. J MULTIVARIATE ANAL 2014. [DOI: 10.1016/j.jmva.2014.04.011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Genovese CR, Perone-Pacifico M, Verdinelli I, Wasserman L. Nonparametric ridge estimation. Ann Stat 2014. [DOI: 10.1214/14-aos1218] [Citation(s) in RCA: 54] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Biau G, Chazal F, Cohen-Steiner D, Devroye L, Rodríguez C. A weighted k-nearest neighbor density estimate for geometric inference. Electron J Stat 2011. [DOI: 10.1214/11-ejs606] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Caillerie C, Chazal F, Dedecker J, Michel B. Deconvolution for the Wasserstein metric and geometric inference. Electron J Stat 2011. [DOI: 10.1214/11-ejs646] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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