Energy statistics: A class of statistics based on distances

Székely, Gábor; Rizzo, Maria L.

doi:10.1016/j.jspi.2013.03.018

Cited by 520 publications

(411 citation statements)

References 37 publications

Supporting

Mentioning

405

Contrasting

Order By: Relevance

“…Then, EFA for each tract average DTI parameter was conducted in the whole sample using the package "psych" (44) and "MVN" (45) in R (46). The relationships between extracted factor scores of the tract average DTI metrics and the cognitive scores were studied using distance correlation performed by the package "energy" in R (47). The Benjamini and Hochberg (1995) false discovery rate (FDR) adjustment was used to adjust P values for multiple comparisons (48).…”

Section: Methodsmentioning

confidence: 99%

Common and heritable components of white matter microstructure predict cognitive function at 1 and 2 y

Lee

Steiner

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Previous studies indicate that the microstructure of individual white matter (WM) tracts is related to cognitive function. More recent studies indicate that the microstructure of individual tracts is highly correlated and that a property common across WM is related to overall cognitive function in adults. However, little is known about whether these common WM properties exist in early childhood development or how they are related to cognitive development. In this study, we used diffusion tensor imaging (DTI) to investigate common underlying factors in 12 fiber tracts, their relationship with cognitive function, and their heritability in a longitudinal sample of healthy children at birth (n = 535), 1 y (n = 322), and 2 y (n = 244) of age. Our data show that, in neonates, there is a highly significant correlation between major WM tracts that decreases from birth to 2 y of age. Over the same period, the factor structure increases in complexity, from one factor at birth to three factors at age 2 y, which explain 50% of variance. The identified common factors of DTI metrics in each age group are significantly correlated with general cognitive scores and predict cognitive ability in later childhood. These factors are moderately heritable. These findings illustrate the anatomical differentiation of WM fiber from birth to 2 y of age that correlate with cognitive development. Our results also suggest that the common factor approach is an informative way to study WM development and its relationship with cognition and is a useful approach for future imaging genetic studies.factor analysis | white matter | DTI | cognition | heritability I ndividual differences in white matter (WM) microstructure have been shown to be related to cognitive functions in adults (1, 2) and children (3-5). Diffusion tensor imaging (DTI) parameters in different WM regions or tracts are variably associated with processing speed, general intelligence, and higher-order cognitive abilities (1-5).To date, the majority of DTI studies of WM microstructure have analyzed each tract or WM region independently. However, more recent studies clearly demonstrate that fractional anisotropy (FA) and other DTI metrics of WM microstructure correlate highly across WM tracts and across a wide age range, including neonates, older children, and adults (6-8). Furthermore, studies indicate that a general factor derived by principal component analyses (PCA) describing common variance in FA across WM tracts is associated with information processing speed (9) as well as general intelligence (10), at least in older adults. In children ages 8 to 16 y, three principal components of FA have been identified; the one corresponding to the corpus callosum was significantly related to IQ (11).The identification of one or more common WM factors that influence variation in multiple WM tracts or regions is important for several reasons. Such factors could prove to be a good target for imaging genetic studies, as one would expect genetic variants influencing WM development and function ...

show abstract

Section: Methodsmentioning

confidence: 99%

Common and heritable components of white matter microstructure predict cognitive function at 1 and 2 y

Lee

Steiner

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…This is called the energy form of the CRPS, since it is just the one-dimensional case of the energy score introduced by Gneiting and Raftery (2007), based on the energy distance of Székely and Rizzo (2013). Taillardat et al (2016) introduced a third expression of the CRPS, valid for continuous forecast CDFs…”

Section: Review Of Available Estimators Of the Crpsmentioning

confidence: 99%

Estimation of the Continuous Ranked Probability Score with Limited Information and Applications to Ensemble Weather Forecasts

Zamo

Naveau

2017

Math Geosci

View full text Add to dashboard Cite

The continuous ranked probability score (CRPS) is a much used measure of performance for probabilistic forecasts of a scalar observation. It is a quadratic measure of the difference between the forecast cumulative distribution function (CDF) and the empirical CDF of the observation. Analytic formulations of the CRPS can be derived for most classical parametric distributions, and be used to assess the efficiency of different CRPS estimators. When the true forecast CDF is not fully known, but represented as an ensemble of values, the CRPS is estimated with some error. Thus, using the CRPS to compare parametric probabilistic forecasts with ensemble forecasts may be misleading due to the unknown error of the estimated CRPS for the ensemble. With simulated data, the impact of the type of the verified ensemble (a random sample or a set of quantiles) on the CRPS estimation is studied. Based on these simulations, recommendations are issued to choose the most accurate CRPS estimator according to the type of ensemble. The interest of these recommendations is illustrated with real ensemble weather forecasts. Also, relationships between several estimators of the CRPS are demonstrated and used to explain the differences of accuracy between the estimators.

show abstract

“…Thus, the dimension of the original matrix was 53 676 rows (213 rows × 252 decades) and 238 columns. The procedure to calculate the E-distance between two clusters, C i , C j of size n i , n j respectively, was that proposed by Szekely and Rizzo (2013).…”

Section: Statistical Analysesmentioning

confidence: 99%

On the use of optical remote sensing to assess phytoplankton biomass dynamics in the Pelagos Sanctuary (Ligurian-Provençal Sea)

Zeichen

Finoia

Shaw

et al. 2017

Regional Studies in Marine Science

View full text Add to dashboard Cite

Energy statistics: A class of statistics based on distances

Cited by 520 publications

References 37 publications

Common and heritable components of white matter microstructure predict cognitive function at 1 and 2 y

Common and heritable components of white matter microstructure predict cognitive function at 1 and 2 y

Estimation of the Continuous Ranked Probability Score with Limited Information and Applications to Ensemble Weather Forecasts

On the use of optical remote sensing to assess phytoplankton biomass dynamics in the Pelagos Sanctuary (Ligurian-Provençal Sea)

Contact Info

Product

Resources

About