Nonparametric Multivariate Descriptive Measures Based on Spatial Quantiles

By Robert Serfling. 2004

87 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2f4378ec33eb3ad1eb0256ffa5ed1bd5f2ea3409

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation (2010, methodology): “Serfling (2004) treats further properties of QS(u, F ) and introduces related nonparametric multivariate descriptive measures for location, spread, skewness, and kurtosis.”
Vector Quantile Regression (2014, background): “Our paper also connects to a number of interesting proposals for performing multivariate quantile regressions, which focus on inheriting certain (though not all) features of univariate quantile regression– for example, minimizing an asymmetric loss, ordering ideas, monotonicity, equivariance or othe”
Multivariate Symmetry and Asymmetry (2006, methodology): “…[15] using projection pursuit and multivariate location regions, [26] and [29], using projection pursuit and the empirical characteristic function, [22] and [54] using Monte Carlo, and [38] and [47] using graphical methods based on statistical depth functions and multivariate quantile functions.”
Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis (2008, background): “Considerations of the notion of depth (Serfling, 2002, 2004, and references therein) might be useful in understanding these ideas more deeply.”
Parametric quantile regression based on the generalized gamma distribution (2013, methodology): “Posterior inference from the pdf given in Stacy and Mirham (1965) was performed using numerical methods organised around Gibbs sampling.”
On the Concept of Depth for Functional Data (2009, methodology): “This depth was also analyzed by Serfling (2004) in the context of spatial rank functions, and it is also closely related and motivated by the geometric quantiles for multivariate data introduced in Sara López-Pintado is Assistant Professor, Department of Economics, Quantitative Methods and…”
Comparison of multivariate distributions using quantile-quantile plots and related tests (2014, background): “The spatial rank of z ∈ Rd with respect to the data cloud formed by the observations X = {x1, . . . ,xn} is defined as n−1 ∑i:xi =z ‖z − xi‖−1(z − xi ) (see, e.g., Möttönen and Oja [29], Chaudhuri [10] and Serfling [32]).”
A Depth Function and a Scale Curve Based on Spatial Quantiles (2002, methodology): “The validity of (12) follows under conditions A1–A3 of Theorem 3.1 of Serfling (2002a).”