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Mini-Workshop: Level Sets and Depth Contours in High Dimensional Data

Mia Hubert, Jun Li, Wolfgang Polonik, Robert Serfling
2011 Oberwolfach Reports  
Foundations for level set estimation as a general statistical method were explored. Deeper understanding of the so-called generalized quantiles approach was pursued.  ...  Another approach is based on multivariate depth functions and inherently addresses issues of robustness.  ...  Data Depth and Multivariate Spacings, Ordering and Beyond Regina Y. Liu (joint work with Juan A.  ... 
doi:10.4171/owr/2011/13 fatcat:ejzs2wp5hnccfn2isy6ihu2hzy

Modeling multivariate ocean data using asymmetric copulas

Yi Zhang, Chul-Woo Kim, Michael Beer, Huliang Dai, Carlos Guedes Soares
2018 Coastal Engineering  
Montes-Iturrizaga and 73 Heredia-Zavoni (2015) have proposed a formulation for expressing the environmental contours as functions 74 of copulas and show that the dependence structure of sea state parameters  ...  A reliable and realistic statistical multivariate model is essential to 15 produce a representative estimate of the sea state for understanding the ocean conditions. Therefore, an 16 ).  ...  The most applicable individual functions are presented in Table 1 . This flexibility can allow this 388 asymmetric copula to be extended to much more complex multivariate models.  ... 
doi:10.1016/j.coastaleng.2018.01.008 fatcat:7dor2wk755dxldjkoo7fp7xlj4

A sequential distance-based approach for imputing missing data: Forward Imputation

Nadia Solaro, Alessandro Barbiero, Giancarlo Manzi, Pier Alda Ferrari
2016 Advances in Data Analysis and Classification  
Three new generalizations to the multivariate case of the convex transform order are defined, namely, the multivariate upper orthant convex, the convex transform order and the conditional convex transform  ...  A new depth function is proposed for this type of data, called multivariate functional halfspace depth.  ... 
doi:10.1007/s11634-016-0243-0 fatcat:yvrqlgllsbesbnvnzzci2egpl4

Analyzing growth trajectories

I. W. McKeague, S. López-Pintado, M. Hallin, M. Šiman
2011 Journal of Developmental Origins of Health and Disease  
This article proposes some new nonparametric approaches to analyzing sparse data on growth trajectories, with flexibility and ease of implementation being key features.  ...  The methods are illustrated using data on participants in the Collaborative Perinatal Project.  ...  Finally, using regression quantiles and Tukey's notion of data depth, we proposed flexible and robust growth charts for multiple variables.  ... 
doi:10.1017/s2040174411000572 pmid:22905314 pmcid:PMC3419544 fatcat:lhimcyfvancypfc56ueybflc74

Computing multiple-output regression quantile regions

Davy Paindaveine, Miroslav Šiman
2012 Computational Statistics & Data Analysis  
In the location case, this procedure allows for computing halfspace depth regions even beyond dimension two.  ...  The corresponding algorithm is described in detail, and illustrations are provided both for simulated and real data.  ...  The quantile contour with known vertices can then be plotted as their convex hull, for example. Such a procedure was also used to generate all figures of this paper.  ... 
doi:10.1016/j.csda.2010.11.014 fatcat:gmw3rcvpbvhmbe6towat2xy4xu

Shape restricted nonparametric regression with Bernstein polynomials

J. Wang, S.K. Ghosh
2012 Computational Statistics & Data Analysis  
The estimation of such shape-restricted regression curves is more challenging for multivariate predictors, especially for functions with compact support.  ...  There has been increasing interest in estimating a multivariate regression function subject to various shape restrictions, such as nonnegativity, isotonicity, convexity and concavity among many others.  ...  The estimator has several advantages over currently available methods for the estimation of multivariate functions with shape restrictions (e.g., non-negativity, monotonicity, and convexity).  ... 
doi:10.1016/j.csda.2012.02.018 fatcat:jzmjnwxpnngehb4zpwmimzxvru

Rejoinder

Marc Hallin, Davy Paindaveine, Miroslav Šiman
2010 Annals of Statistics  
Rejoinder to "Multivariate quantiles and multiple-output regression quantiles: From L_1 optimization to halfspace depth" by M. Hallin, D. Paindaveine and M. Siman [arXiv:1002.4486]  ...  If L-estimation is to be privileged, point-valued quantiles, which provide easily tractable integrands for L-functionals, may look more attractive.  ...  . , 14, along with, for all ℓ, (i) the halfspace depth contour of order 1/n (in green), that is, the convex hull of the sample, and (ii) the (τ u0)-quantile hyperplane (in black) obtained for τ = 2.5/n  ... 
doi:10.1214/09-aos723rej fatcat:xmlfsys2qjgmbfc5gcw3hh3qv4

Asymptotically exact data augmentation: models, properties and algorithms [article]

Maxime Vono and Nicolas Dobigeon and Pierre Chainais
2020 arXiv   pre-print
Supplementary materials including computer code for this paper are available online.  ...  Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference  ...  Let ψ a continuously-differentiable and strictly convex function defined on a closed convex set.  ... 
arXiv:1902.05754v3 fatcat:mn3ezsf3hfhsfjol4z4hk36hxu

The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey'shTransformation as a Special Case

Georg M. Goerg
2015 The Scientific World Journal  
The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data.  ...  It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey'shpdf and cdf.  ...  Quantile Function. Quantile fitting has been the standard technique to estimate , , and of Tukey's ℎ. In particular, the medians of and are equal.  ... 
doi:10.1155/2015/909231 pmid:26380372 pmcid:PMC4562338 fatcat:hw663r7vtbfovcuz233djiirci

Multivariate Conditional Transformation Models [article]

Nadja Klein, Torsten Hothorn, Luisa Barbanti, Thomas Kneib
2020 arXiv   pre-print
We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way  ...  to existing benchmarks such that complex truly multivariate data-generating processes can be inferred from observations.  ...  Acknowledgements The authors thank two referees and an associate editor for helpful comments that improved  ... 
arXiv:1906.03151v3 fatcat:7nq3lakekrd3ld3jwh7gv5gjaq

Exponential-family embedding with application to cell developmental trajectories for single-cell RNA-seq data [article]

Kevin Lin, Jing Lei, Kathryn Roeder
2020 bioRxiv   pre-print
Scientists often embed cells into a lower-dimensional space when studying single-cell RNA-seq data for improved downstream analyses such as developmental trajectory analyses, but the statistical properties  ...  Using the eSVD estimated embedding, we then investigate the cell developmental trajectories of the oligodendrocytes.  ...  The contour of the densities estimated based on the MASS::kde2d function (using the default bandwidth), where the level of the contour is chosen to be the 92.5% quantile of the estimated density across  ... 
doi:10.1101/2020.09.25.313882 fatcat:hh2yozywkrcltdwyibzeoy67ma

Modelling skewed spatial random fields through the spatial vine copula

Benedikt Gräler
2014 Spatial Statistics  
All approaches use the same two types of marginal quantile functions.  ...  To increase the number of data pairs in the estimation of the consecutive spatial trees, it is beneficial to use a neighbourhood extending beyond the dimension of the spatial vine copula (d ≤d) thus adding  ... 
doi:10.1016/j.spasta.2014.01.001 fatcat:o3xerfpzfjhdhgnonc5lz2qwk4

Depth and Depth-Based Classification with R Package ddalpha

Oleksii Pokotylo, Pavlo Mozharovskyi, Rainer Dyckerhoff
2019 Journal of Statistical Software  
The implemented functions for depth visualization and the built-in benchmark procedures may also serve to provide insights into the geometry of the data and the quality of pattern recognition.  ...  These can be further used in the depth-based multivariate and functional classifiers implemented in the package, where the DDα-procedure is in the main focus.  ...  Acknowledgments The authors highly appreciate the help of Karl Mosler consisting in numerous remarks on earlier versions of this article and his notable contributions to the field of data depth.  ... 
doi:10.18637/jss.v091.i05 fatcat:7lqc4fnxjzf7tihrxnvnataqry

Depth and depth-based classification with R-package ddalpha [article]

Oleksii Pokotylo, Pavlo Mozharovskyi, Rainer Dyckerhoff
2016 arXiv   pre-print
The implemented functions for depth visualization and the built-in benchmark procedures may also serve to provide insights into the geometry of the data and the quality of pattern recognition.  ...  These can be further used in the depth-based multivariate and functional classifiers implemented in the package, where the DDα-procedure is in the main focus.  ...  Acknowledgments The authors want to thank Karl Mosler for his valuable suggestions that have substantially improved the present work.  ... 
arXiv:1608.04109v1 fatcat:2jj5kg3harhqfnvf2adc4ixw2a

Multivariate Ranks and Quantiles using Optimal Transport: Consistency, Rates, and Nonparametric Testing [article]

Promit Ghosal, Bodhisattva Sen
2021 arXiv   pre-print
We also provide a sub-Gaussian tail bound for the global L_2-loss of the empirical quantile function.  ...  We study the characterization, computation and properties of the multivariate rank and quantile functions and their empirical counterparts.  ...  Denote the multivariate quantile/rank functions for ν n by Q n and R n .  ... 
arXiv:1905.05340v3 fatcat:emm2s2x6izevhhpecigca5b3by
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