On asymptotic distributions of several test statistics for familial relatedness in linear mixed models

DeVogel, Nicholas; Auer, Paul L.; Manansala, Regina; Wang, Tao

doi:10.1002/sim.9762

Cited by 1 publication

(1 citation statement)

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“…By introducing a more general assumption of the multivariate variance distribution, the existing bounds of linear eigenvalue statistics for random matrix ensemble were re-established [26]. For testing the additive effect of the expected familial relatedness, according to a dataset from the UK Biobank, a study was conducted based on LES [27] where the four test statistics, the likelihood ratio test (LRT), the restricted likelihood ratio test (RLRT), and the sequence kernel association test (SKAT) statistics were employed. For ozone measurements, Han proposed an LES statistical estimation in which the LES-associated test function included a log-determinant, the trace of the matrix inverse, the Estrada index, and the Schatten p-norm to estimate over 6 million variables [28].…”

Section: Related Workmentioning

confidence: 99%

A Deep Learning Neural Network Method Using Linear Eigenvalue Statistics for Schizophrenic EEG Data Classification

Liu,

Li,

et al. 2023

Mathematics

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Electroencephalography (EEG) signals can be used as a neuroimaging indicator to analyze brain-related diseases and mental states, such as schizophrenia, which is a common and serious mental disorder. However, the main limiting factor of using EEG data to support clinical schizophrenia diagnosis lies in the inadequacy of both objective characteristics and effective data analysis techniques. Random matrix theory (RMT) and its linear eigenvalue statistics (LES) can provide an effective mathematical modeling method for exploring the statistical properties of non-stationary nonlinear systems, such as EEG signals. To obtain an accurate classification and diagnosis of schizophrenia, this paper proposes a LES-based deep learning network scheme in which a series of random matrixes, consisting of EEG data sliding window sampling and their eigenvalues, are employed as features for deep learning. Due to the fact that the performance of the LES-based scheme is sensitive to the LES’s test function, the proposed LES-based deep learning network is embedded with two ways of combining LES’s test functions with learning techniques: the first is to have the LES’s test function assigned, while, using the second way, the optimal LES’s test function should be solved in a functional optimization problem. In this paper, various test functions and different optimal learning methods were coupled in experiments. Our results revealed a binary classification accuracy of nearly 90% in distinguishing between healthy controls (HC) and patients experiencing the first episode of schizophrenia (FES). Additionally, we achieved a ternary classification accuracy of approximately 70% by including clinical high risk for psychosis (CHR). The LES-embedded approach yielded notably higher classification accuracy compared to conventional machine learning methods and standard convolutional neural networks. As the performance of schizophrenia classification is strongly influenced by test functions, a functional optimization problem was proposed to identify an optimized test function, and an approximated parameter optimization problem was introduced to limit the search area of suitable basis functions. Furthermore, the parameterization test function optimization problem and the deep learning network were coupled to be synchronously optimized during the training process. The proposal approach achieved higher classification accuracy rates of 96.87% between HC and FES, with an additional 89.06% accuracy when CHR was included. The experimental studies demonstrated that the proposed LES-based method was significantly effective for schizophrenic EEG data classification.

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Section: Related Workmentioning

confidence: 99%