Asymptotic efficiency of exponentiality tests based on order statistics characterization

2010 ◽  
Vol 17 (4) ◽  
pp. 749-763
Author(s):  
Ya. Yu. Nikitin ◽  
Ksenia Yu. Volkova
Keyword(s):  
Large Deviations ◽  
Order Statistics ◽  
Asymptotic Efficiency ◽  
Bahadur Efficiency ◽  
Limiting Distributions ◽  
Scale Invariant ◽  
New Statistics

Abstract We propose new scale-invariant tests for exponentiality based on the characterization in terms of order statistics. Limiting distributions and large deviations of new statistics are described and their local Bahadur efficiency for common alternatives is calculated.

scholarly journals Recursive dynamic functional connectivity reveals a characteristic correlation structure in human scalp EEG

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Siddharth Panwar ◽  
Shiv Dutt Joshi ◽  
Anubha Gupta ◽  
Sandhya Kunnatur ◽  
Puneet Agarwal
Keyword(s):  
Functional Connectivity ◽  
Order Statistics ◽  
Correlation Structure ◽  
Connectivity Pattern ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Scale Invariant ◽  
Dynamic Functional Connectivity ◽  
Neurophysiological Data ◽  
Show Evidence

AbstractTime-varying neurophysiological activity has been classically explored using correlation based sliding window analysis. However, this method employs only lower order statistics to track dynamic functional connectivity of the brain. We introduce recursive dynamic functional connectivity (rdFC) that incorporates higher order statistics to generate a multi-order connectivity pattern by analyzing neurophysiological data at multiple time scales. The technique builds a hierarchical graph between various temporal scales as opposed to traditional approaches that analyze each scale independently. We examined more than a million rdFC patterns obtained from morphologically diverse EEGs of 2378 subjects of varied age and neurological health. Spatiotemporal evaluation of these patterns revealed three dominant connectivity patterns that represent a universal underlying correlation structure seen across subjects and scalp locations. The three patterns are both mathematically equivalent and observed with equal prevalence in the data. The patterns were observed across a range of distances on the scalp indicating that they represent a spatially scale-invariant correlation structure. Moreover, the number of patterns representing the correlation structure has been shown to be linked with the number of nodes used to generate them. We also show evidence that temporal changes in the rdFC patterns are linked with seizure dynamics.

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