Descriptive measures of multivariate scatter and linear dependence

By D. Pena, Julio Rodríguez. 2003

81 citations recorded by the source corpus.

In this paper we propose two new descriptive measures for multivariate data: the effective variance and the effective dependence. These measures have a direct geometric and statistical interpretation and can be used to compare groups with different number of variables. The contribution of these measures to understanding multivariate data is illustrated by several examples.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e4a65bb965fe75ffa96031b562c1b1e8f240f79e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Pena
2. Qiwei Yao

In Statistics and Probability

1. D. Pena
2. Julio Rodríguez
3. A. Ian McLeod
4. Esam Mahdi
5. Yingye Zheng
6. Adrian E. Raftery

Citations in the corpus

• The log of the determinant of the autocorrelation matrix for testing goodness of fit in time series (2006, background): “Peña and Rodríguez (2002), based on a general measure of multivariate dependence, the Effective Dependence, see Peña and Rodríguez (2003), proposed a portmanteau test by applying this measure to the autocorrelation matrix, leading to the statistic D̂m = T [1 − |R̂m|1/m], (3) where R̂m is R̂m = ⎡⎢⎢⎣…”
• Multivariate Process Variability Monitoring (2008, unknown): “Other examples, such as the effective variance (Pena and Rodriguez, 2005; Serfling, 1980), square root of GV (Alt and Smith, 1988), and relative GV (Tang and Barnett, 1996), are variants of GV.”