Measuring and testing dependence by correlation of distances

Székely, Gábor; Rizzo, Maria L.; Бакиров, Н. К.

doi:10.1214/009053607000000505

Cited by 2,038 publications

(2,115 citation statements)

References 13 publications

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“…The correlation between GPP sat and climate variables was tested with distance correlation 33 . Distance correlation is a measure of statistical dependence between random variables and here we tested the dependence between GPP sat and temperature and WAI jointly.…”

Section: Resultsmentioning

confidence: 99%

Stand age and species richness dampen interannual variation of ecosystem-level photosynthetic capacity

et al. 2017

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The total uptake of carbon dioxide by ecosystems via photosynthesis (gross primary productivity, GPP) is the largest flux in the global carbon cycle. A key ecosystem functional property determining GPP is the photosynthetic capacity at light saturation (GPPsat), and its interannual variability (IAV) is propagated to the net land–atmosphere exchange of CO2. Given the importance of understanding the IAV in CO2 fluxes for improving the predictability of the global carbon cycle, we have tested a range of alternative hypotheses to identify potential drivers of the magnitude of IAV in GPPsat in forest ecosystems. Our results show that while the IAV in GPPsat within sites is closely related to air temperature and soil water availability fluctuations, the magnitude of IAV in GPPsat is related to stand age and biodiversity (R2 = 0.55, P < 0.0001). We find that the IAV of GPPsat is greatly reduced in older and more diverse forests, and is higher in younger forests with few dominant species. Older and more diverse forests seem to dampen the effect of climate variability on the carbon cycle irrespective of forest type. Preserving old forests and their diversity would therefore be beneficial in reducing the effect of climate variability on Earth's forest ecosystems

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Section: Resultsmentioning

confidence: 99%

Stand age and species richness dampen interannual variation of ecosystem-level photosynthetic capacity

et al. 2017

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“…In the next step, following Székely et al (2007), we use the distance correlation in order to analyze linear and non-linear dependency between the FCI, and its bank and debt components, and the role of money on output. We …nd that the Pearson correlation coe¢ cient is only sensitive to linear relationships between two variables, whereas it can easily be zero for the dependent variables.…”

Section: Discussionmentioning

confidence: 99%

Money and monetary policy in Israel during the last decade

Benchimol¹

2016

Journal of Policy Modeling

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This study examines how money and monetary policy have in‡uenced output and in ‡ation during the past decade in Israel by comparing two New Keynesian DSGE models. One is a baseline separable model (Galí, 2008) and the other assumes non-separable household preferences between consumption and money (Benchimol and Fourçans, 2012). We test both models by using rolling window Bayesian estimations over the last decade (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013). The results of the presented dynamic analysis show that the sensitivity of output with respect to money shocks increased during the Dot-com, Intifada, and Subprime crises. The role of monetary policy increased during these crises, especially with regard to in ‡ation, even though the effectiveness of conventional monetary policy decreased during the Subprime crisis. In addition, the non-separable model including money provides lower forecast errors than the baseline separable model without money, while the in ‡uence of money on output ‡uctuations can be seen as a good predictive indicator of bank and debt risks. By impacting and monitoring households'money holdings, policy makers could improve their forecasts and crisis management through models considering monetary aggregates.

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“…The first four are based on Pearson correlation, Kendall's rank correlation, the distance correlation (Székely et al, 2007) and the rank-based distance correlation (Székely and Rizzo, 2009), respectively. The distance correlation and rank-based distance correlation are also nonnegative with equality to zero if and only if two random variables are independent.…”

Section: An Estimationmentioning

confidence: 99%

Model-Free Feature Screening for Ultrahigh Dimensional Data through a Modified Blum-Kiefer-Rosenblatt Correlation

Zhu¹,

Zhou²

2018

STAT SINICA

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In this paper we introduce a modified Blum-Kiefer-Rosenblatt correlation (MBKR for short) to rank the relative importance of each predictor in ultrahigh dimensional regressions. We advocate using the MBKR for two reasons. First, the MBKR is nonnegative and equals zero if and only if two random variables are independent, indicating that the MBKR can detect nonlinear dependence. We illustrate that the sure independence screening procedure based on the MBKR (MBKR-SIS for short) is effective to detect nonlinear effects including interactions and heterogeneity, particularly when both continuous and discrete predictors are involved simultaneously. Second, the MBKR is conceptually simple, easy to implement and affine-invariant. The MBKR is free of tuning parameters and no iteration is required in estimation. It remains unchanged when order-preserving transformations are applied to the response or predictors, indicating that the MBKR-SIS is robust to the presence of extreme values and outliers in the observations. We also show that, under mild conditions, the MBKR-SIS procedure has the desirable sure screening and ranking consistency properties, Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) Feature Screening via Modified Blum-Kiefer-Rosenblatt Correlation 2 which guarantee that all important predictors can be retained after screening with probability approaching one. We also propose an iterative screening procedure to detect the important predictors which are marginally independent of the response variable. We demonstrate the merits of the MBKR-SIS procedure through simulations and an application to a real-world dataset.

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Measuring and testing dependence by correlation of distances

Cited by 2,038 publications

References 13 publications

Stand age and species richness dampen interannual variation of ecosystem-level photosynthetic capacity

Stand age and species richness dampen interannual variation of ecosystem-level photosynthetic capacity

Money and monetary policy in Israel during the last decade

Model-Free Feature Screening for Ultrahigh Dimensional Data through a Modified Blum-Kiefer-Rosenblatt Correlation

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