A Survey of Multidimensional Medians

Small, Christopher G.

doi:10.2307/1403809

Cited by 317 publications

(182 citation statements)

References 40 publications

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“…In more than one dimension, the concepts of order statistics and ranks are more involved and several definitions have been proposed in Mahalanobis (1936), Tukey (1975), Brown (1983), Oja (1983), Liu (1988Liu ( ,1990, Small (1990), Gordaliza (1991), Singh(1991), Donoho and Gasko (1992), Liu and Singh (1993), Cuesta-Albertos, Gordaliza and Matrán (1997) and Fraiman and Meloche (1999).…”

Section: Introductionmentioning

confidence: 99%

Trimmed means for functional data

Fraiman

Muñiz

2001

Test

284

257

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In practice, the use of functional data is often preferable to that of large finite-dimensional vectors obtained by discrete approximations of functions. In this paper a new concept of data depth is introduced for functional data. The aim is to measure the centrality of a given curve within a group of curves. This concept is used to define ranks and trimmed means for functional data. Some theoretical and practical aspects are discussed and a simulation study is given. The results show a good performance of our method, in terms of efficiency and robustness, when compared with the mean. Finally, a real-data example based on the Nasdaq 100 index is discussed.

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Section: Introductionmentioning

confidence: 99%

Trimmed means for functional data

Fraiman

Muñiz

2001

Test

284

257

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“…In the 1-D Box Plot concept, the central tendency [13] of the dataset is represented using the median value. For 2D values, three different approaches can be used to define and visualize this tendency.…”

Section: Central Tendencymentioning

confidence: 99%

State of the Art in Patterns for Point Cluster Analysis

Emmanuel

Devogèle

McArdle

2014

Computational Science and Its Applications – ICCSA 2014

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Abstract. Nowadays, an abundance of sensors are used to collect very large datasets containing spatial points which can be mined and analyzed to extract meaningful patterns. In this article, we focus on different techniques used to summarize and visualize 2D point clusters and discuss their relative strengths. This article focuses on patterns which describe the dispersion of data around a central tendency. These techniques are particularly beneficial for detecting outliers and understanding the spatial density of point clusters.

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“…• suppression of impulsive noise while preserving edges [8] • non-parametric estimator for the center of a distribution [9] • converging behavior for iterated application [10] • fast algorithms [11] Therefore the median seems to be an appropriate method to reduce noise level in the label images. On simulated data, a good convergence was reached after two iterations.…”

Section: Different Values Such Intermediate Label Values Can Either mentioning

confidence: 99%