On Robust Estimation of a Correlation Coefficient and Correlation Matrix

Shevlyakov, Georgy; Khvatova, Tatiana

doi:10.1007/978-3-642-58988-1_17

Cited by 13 publications

(15 citation statements)

References 8 publications

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“…Previous studies have shown a model order of 20 to be sufficient for whitening signals (Santosa, Aarabi, Perlman, & Huppert, 2017). The robust correlation coefficients were calculated between participants using the robust regression approach (Shevlyakov & Smirnov, 2011), in which the geometric mean is taken of the robust regression coefficients obtained from regressing channel X onto channel Y and vice versa, for example,

r = \sqrt{{\overset{β}{true}}_{X \to Y} {\overset{β}{true}}_{Y \to X}}

. Synchronization was then quantified using the Fisher r ‐to‐ z transform of the absolute value of the robust correlation coefficient.…”

Section: Methodsmentioning

confidence: 99%

Parent–child neural synchrony: a novel approach to elucidating dyadic correlates of preschool irritability

Quiñones‐Camacho

Fishburn

Camacho

et al. 2019

Child Psychology Psychiatry

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Background: Research to date has largely conceptualized irritability in terms of intraindividual differences. However, the role of interpersonal dyadic processes has received little consideration. Nevertheless, difficulties in how parentchild dyads synchronize during interactions may be an important correlate of irritably in early childhood. Innovations in developmentally sensitive neuroimaging methods now enable the use of measures of neural synchrony to quantify synchronous responses in parent-child dyads and can help clarify the neural underpinnings of these difficulties. We introduce the Disruptive Behavior Diagnostic Observation Schedule: Biological Synchrony (DB-DOS:BioSync) as a paradigm for exploring parent-child neural synchrony as a potential biological mechanism for interpersonal difficulties in preschool psychopathology. Methods: Using functional near-infrared spectroscopy (fNIRS) 4-to 5year-olds (N = 116) and their mothers completed the DB-DOS:BioSync while assessing neural synchrony during mild frustration and recovery. Child irritability was measured using a latent irritability factor that was calculated from four developmentally sensitive indicators. Results: Both the mild frustration and the recovery contexts resulted in neural synchrony. However, less neural synchrony during the recovery context only was associated with more child irritability. Conclusions: Our results suggest that recovering after a frustrating period might be particularly challenging for children high in irritability and offer support for the use of the DB-DOS:BioSync task to elucidate interpersonal neural mechanisms of developmental psychopathology.

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r = \sqrt{{\overset{β}{true}}_{X \to Y} {\overset{β}{true}}_{Y \to X}}

. Synchronization was then quantified using the Fisher r ‐to‐ z transform of the absolute value of the robust correlation coefficient.…”

Section: Methodsmentioning

confidence: 99%

Parent–child neural synchrony: a novel approach to elucidating dyadic correlates of preschool irritability

Quiñones‐Camacho

Fishburn

Camacho

et al. 2019

Child Psychology Psychiatry

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“…Robust correlation approaches are used to control for the leverage of outliers. The review paper by Pasman and Shevlyakov 60 describes a number of different approaches for robust estimates of correlation. In this work, we use a robust regression approach to estimating robust correlation, 60 which closely follows the work we have previously proposed for analysis of functional time-series fNIRS data in Barker et al.…”

Section: Theorymentioning

confidence: 99%

“…In this paper, we use the regression model since we feel that is easier to devise extensions needed to extend the mathematical notation to cover multivariate models, including Grangers causality. However, the review by Shevlyakov and Smirnov 60 offers several other formulations to this robust correlation problem, which could be explored in future work.…”

Section: Theorymentioning

confidence: 99%

Characterization and correction of the false-discovery rates in resting state connectivity using functional near-infrared spectroscopy

et al. 2017

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, "Characterization and correction of the false-discovery rates in resting state connectivity using functional near-infrared spectroscopy," J. Biomed. Opt. 22(5), 055002 (2017), doi: 10.1117/1.JBO.22.5.055002. Abstract. Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of red to near-infrared light to measure changes in cerebral blood oxygenation. Spontaneous (resting state) functional connectivity (sFC) has become a critical tool for cognitive neuroscience for understanding task-independent neural networks, revealing pertinent details differentiating healthy from disordered brain function, and discovering fluctuations in the synchronization of interacting individuals during hyperscanning paradigms. Two of the main challenges to sFC-NIRS analysis are (i) the slow temporal structure of both systemic physiology and the response of blood vessels, which introduces false spurious correlations, and (ii) motionrelated artifacts that result from movement of the fNIRS sensors on the participants' head and can introduce non-normal and heavy-tailed noise structures. In this work, we systematically examine the false-discovery rates of several time-and frequency-domain metrics of functional connectivity for characterizing sFC-NIRS. Specifically, we detail the modifications to the statistical models of these methods needed to avoid high levels of falsediscovery related to these two sources of noise in fNIRS. We compare these analysis procedures using both simulated and experimental resting-state fNIRS data. Our proposed robust correlation method has better performance in terms of being more reliable to the noise outliers due to the motion artifacts. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…On the other hand, it is necessary to study these problems due to their widespread occurrence (estimation of correlation and covariance matrices in regression and multivariate analysis, estimation of correlation functions of stochastic processes, etc. ), and also due to great instability of classical methods of estimation with outliers in the data (Devlin et al, 1975;Gnanadesikan and Kettenring, 1972;Huber, 1981;Pasman and Shevlyakov, 1987;Rocke and Woodruff, 1996;Rousseeuw and Leroy, 1987;Shevlyakov, 1997a;Shevlyakov and Khvatova, 1998b).…”

Section: Introductory Remarksmentioning

confidence: 99%

Robustness in Data Analysis

Shevlyakov¹,

Vilchevski²

2001

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v vi statistics. Chapter 2 gives a new probability-free approach to constructing optimisation criteria in data analysis. Chapter 3 contains new results on robust minimax (in the Huber sense) estimation of location over the distribution classes with bounded variances and subranges, as well as for the classes of lattice distributions. Chapter 4 is confined to robust estimation of scale. Chapter 5 deals with robust regression and autoregression problems. Chapter 6 covers the particular case of L 1-norm estimation. Chapter 7 treats robust estimation of correlation. Chapter 8 introduces and discusses data analysis technologies, and Chapter 9 represents applications. We would like to express our deep appreciation to I. B. Chelpanov, E. P. Guilbo, B. T. Polyak, and Ya. Z. Tsypkin who attracted our attention to robust statistics. We are grateful to S. A. Aivazyan and L. D. Meshalkin for discussions and comments of our results at their seminars in the Central Institute of Economics and Mathematics of Russian Academy of Sciences (Moscow). We are very grateful to A. V. Kolchin for his great help in the preparation of this book. Finally, we highly appreciate V. Yu. Korolev and V. M. Zolotarev for their attention to our work and, in general, to such an important field of mathematical statistics as robustness.

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On Robust Estimation of a Correlation Coefficient and Correlation Matrix

Cited by 13 publications

References 8 publications

Parent–child neural synchrony: a novel approach to elucidating dyadic correlates of preschool irritability

Parent–child neural synchrony: a novel approach to elucidating dyadic correlates of preschool irritability

Characterization and correction of the false-discovery rates in resting state connectivity using functional near-infrared spectroscopy

Robustness in Data Analysis

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