Assessing extremal dependence of environmental spatial fields

1. The auditory responses of 207 single neurons in the intermediate and deep layers of the superior colliculus (SC) of barbiturate -or chloralose-anesthetized cats were recorded extracellularly. Sealed stimulating systems incorporating calibrated probe microphone assemblies were employed to present tone- and noise-burst stimuli. 2. All acoustically activated neurons responded with onset responses to noise bursts. Of those neurons also tested with tonal stimuli, approximately 30% were unresponsive over the frequency range tested (0.1-40 kHz), while the others had higher thresholds to tones than to noise. 3. Details of frequency responsiveness were obtained for 55 neurons; 21 were broadly tuned, while 34 were sharply tuned with clearly defined characteristic frequencies (CFs). All sharply tuned neurons had CFs greater than or equal to 10 kHz. 4. The majority of neurons (81%) responded with latencies in the range 8-20 ms; only 11% of neurons had latencies greater than 30 ms. 5. Binaural response properties were examined for 165 neurons. The great majority (79%) received monaural excitatory input only from the contralateral ear (EO). However, most EO cells were binaurally influenced, the contralateral response being either inhibited (EO/I; 96 of 131 units) or facilitated (EO/F; 33 of 131 units) by simultaneous ipsilateral stimulation. Small subgroups were monaurally excited by either ear (EE cells; 8%) or were unresponsive monaurally but responded strongly to binaural stimulation (OO/F cells; 7%). 6. EO/I, EO/F, and OO/F neurons showed characteristic forms of sensitivity to interaural intensity differences (IIDs). The IID functions of EO/I neurons would be expected to produce large contralateral spatial receptive fields with clearly defined medial borders, such as have been described in studies of deep SC neurons employing free-field stimuli. 7. Preliminary evidence suggests a possible topographic organization of IID sensitivity in deep SC, such that the steeply sloping portion of the function (corresponding to the medial edge of the receptive field) is shifted laterally for EO/I neurons located more caudally in the nucleus. 8. The auditory properties of deep SC neurons are compared with previous reports and implications for the organization of auditory input are considered. The binaural properties and auditory spatial fields of deep SC neurons suggest that any representation of auditory space in this structure is unlikely to be based on restricted spatial fields.

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Markets liquidity risk under extremal dependence: Analysis with VaRs methods

Economic Modelling ◽

10.1016/j.econmod.2012.05.036 ◽

2012 ◽

Vol 29 (5) ◽

pp. 1830-1836 ◽

Cited By ~ 6

Author(s):

Awatef Ourir ◽

Wafa Snoussi

Keyword(s):

Liquidity Risk ◽

Dependence Analysis ◽

Extremal Dependence

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ON THE EXTREMAL DEPENDENCE COEFFICIENTS OF GAUSSIAN DISTRIBUTIONS

Vestnik NSUEM ◽

10.34020/2073-6495-2021-1-161-167 ◽

2021 ◽

pp. 161-167

Author(s):

S. E. Khrushchev

Keyword(s):

Close Correlation ◽

Gaussian Copula ◽

Marginal Distributions ◽

Gaussian Distributions ◽

Extremal Dependence ◽

Zero Values ◽

Coronavirus Infection ◽

The Russian Federation ◽

The One ◽

The Relationship

The paper considers a way to represent the relationship between indicators in the form of copulas. Copulas are popular mathematical tools. This is due to the fact that, on the one hand, the marginal distributions of indicators are divided in the copulas, and on the other hand, the structure of the relationship between these marginal distributions is divided, which makes it possible to very effectively study the connections that arise in real populations. Special attention in the work is paid to extremal dependence coefficients - important numerical characteristics of the connection in conditions of extreme small or extremely large values of indicators. It is shown that even under conditions of close correlation between the indices for a two-dimensional Gaussian distribution, the lower and upper coefficients of the extreme dependence take zero values. This indicates the impossibility of predicting the values of one indicator when fixing too small or too large values of another indicator. This work shows that the relationship between the number of COVID-19 coronavirus infections per 100,000 people and the number of deaths from COVID-19 coronavirus infection per 100,000 people in the regions of the Russian Federation can be represented in the form of a Gaussian copula.

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Nonparametric Estimation of Extremal Dependence Anna Kiriliouk, Johan Segers, and Michał Warchoł

Extreme Value Modeling and Risk Analysis ◽

10.1201/b19721-21 ◽

2016 ◽

pp. 373-396 ◽

Cited By ~ 1

Keyword(s):

Nonparametric Estimation ◽

Extremal Dependence

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Extremal Dependence between Temperature and Ozone over the Continental U.S.

10.5194/acp-2017-1033 ◽

2017 ◽

Author(s):

Pakawat Phalitnonkiat ◽

Wenxiu Sun ◽

Mircea D. Grigoriu ◽

Peter G. M. Hess ◽

Gennady Samorodnitsky ◽

...

Keyword(s):

Climate Model ◽

Heat Waves ◽

Strong Dependence ◽

Measurement Data ◽

The United States ◽

Value Theory ◽

Temperature Extremes ◽

Measured Temperature ◽

Extremal Dependence ◽

Year 2000

Abstract. The co-occurrence of heat waves and pollution events and the resulting high mortality rates emphasizes the importance of the co-occurrence of pollution and temperature extremes. Through the use of extreme value theory and other statistical methods ozone and temperature extremes and their joint occurrence are analyzed over the United States during the summer months (JJA) using Clean Air Status and Trends Network (CASTNET) measurement data and simulations of the present and future climate and chemistry in the Community Earth System Model (CESM1) CAM4-chem. Three simulations using CAM4-chem were analyzed: the Chemistry Climate Model Initiative (CCMI) reference experiment using specified dynamics (REFC1SD) between 1992–2010, a 25-year present-day simulation branched off the CCMI REFC2 simulation in the year 2000 and a 25-year future simulation branched off the CCMI REFC2 simulation in 2100. The latter two simulations differed in their concentration of carbon dioxide (representative of the years 2000 and 2100) but were otherwise identical. A new metric is developed to measure the joint extremal dependence of ozone and temperature by evaluating the spectral dependence of their extremes. Two regions of the U.S. give the strongest measured extreme dependence of ozone and temperature: the northeast and the southeast. The simulations do not capture the relationship between temperature and ozone over the northeast but do simulate a strong dependence of ozone on extreme temperatures over the southeast. In general, the simulations of ozone and temperature do not capture the width of the measured temperature and ozone distributions. While on average the future increase in the 90th percentile temperature and the 90th percentile ozone slightly exceed the mean increase over the continental U.S., in many regions the width of the temperature and ozone distributions decrease. The location of future increases in the tails of the ozone distribution are weakly related to those of temperature with a correlation of 0.3.

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Extremal dependence of random scale constructions

Extremes ◽

10.1007/s10687-019-00353-3 ◽

2019 ◽

Vol 22 (4) ◽

pp. 623-666 ◽

Cited By ~ 3

Author(s):

Sebastian Engelke ◽

Thomas Opitz ◽

Jennifer Wadsworth

Keyword(s):

Extremal Dependence ◽

Random Scale

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Significant Extremal Dependence of a Daily North Atlantic Oscillation Index (NAOI) and Weighted Regionalised Rainfall in a Small Island Using the Extremogram

Water ◽

10.3390/w12112989 ◽

2020 ◽

Vol 12 (11) ◽

pp. 2989

Author(s):

Luis Angel Espinosa ◽

Maria Manuela Portela ◽

Rui Rodrigues

Keyword(s):

North Atlantic Oscillation ◽

North Atlantic ◽

North Atlantic Oscillation Index ◽

Climate Models ◽

Global Climate ◽

Global Climate Models ◽

Statistical Dependence ◽

Small Island ◽

Extremal Dependence ◽

Rain Gauges

Extremal dependence or independence may occur among the components of univariate or bivariate random vectors. Assessing which asymptotic regime occurs and also its extent are crucial tasks when such vectors are used as statistical models for risk assessment in the field of Climatology under climate change conditions. Motivated by the poor resolution of current global climate models in North Atlantic Small Islands, the extremal dependence between a North Atlantic Oscillation index (NAOI) and rainfall was considered at multi-year dominance of negative and positive NAOI, i.e., −NAOI and +NAOI dominance subperiods, respectively. The datasets used (from 1948–2017) were daily NAOI, and three daily weighted regionalised rainfall series computed based on factor analysis and the Voronoi polygons method from 40 rain gauges in the small island of Madeira (∼740 km2), Portugal. The extremogram technique was applied for measuring the extremal dependence within the NAOI univariate series. The cross-extremogram determined the dependence between the upper tail of the weighted regionalised rainfalls, and the upper and lower tails of daily NAOI. Throughout the 70-year period, the results suggest systematic evidence of statistical dependence over Madeira between exceptionally −NAOI records and extreme rainfalls, which is stronger in the −NAOI dominance subperiods. The extremal dependence for +NAOI records is only significant in recent years, however, with a still unclear +NAOI dominance.

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