Two-Sample Tests Based on Data Depth

Article Statistics & Probability

Choosing Among Notions of Multivariate Depth Statistics

Karl Mosler et al.

Summary: This article discusses the measurement of outliers in multivariate data and the concept of multivariate depth function. The choice of depth statistic requires a trade-off between invariance, robustness, and computational feasibility. The complexity and speed of exact algorithms are compared, and the accuracy of approximate approaches is discussed. The article also briefly addresses extensions to local and functional depths and connections to regression depth.

STATISTICAL SCIENCE (2022)

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Article Statistics & Probability

Depth for Curve Data and Applications

Pierre Lafaye de Micheaux et al.

Summary: Tukey defined statistical data depth in 1975, which has evolved into a powerful tool useful in various scientific fields. Recently, the extension of data depth concept to the functional setting has attracted attention from theoretical and applied statisticians. The notion of data depth suitable for curves or trajectories, independent of parameterization, has been proposed and applied in various applications such as brain imaging and pattern recognition.

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (2021)

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Article Statistics & Probability

Illumination Depth

Stanislav Nagy et al.

Summary: The concept of illumination in convex geometry is used to refine the halfspace depth for multivariate data, providing finer resolution for sample points and breaking ties in depth-based ordering. It introduces a depth-like function for points outside the convex hull of the support of the probability measure and aligns well with common probability distributions.

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS (2021)

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Article Statistics & Probability

On General Notions of Depth for Regression

Yijun Zuo

Summary: This article discusses the current research status and related issues of location depth and regression depth concepts, focusing on the relationship between Carrizosa depth and RD of RH99, as well as the possible advantages and limitations of existing depth concepts.

STATISTICAL SCIENCE (2021)

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Article Agriculture, Multidisciplinary