Randomized estimation of functional covariance operator via subsampling

Stat ◽  
2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Shiyuan He ◽  
Xiaomeng Yan
Keyword(s):  
Covariance Operator

On a Class of Covariance Operators

1998 ◽  
Vol 5 (5) ◽  
pp. 415-424
Author(s):  
T. Chantladze ◽  
N. Kandelaki
Keyword(s):  
Complete Classification ◽  
Covariance Operator ◽  
Random Vectors ◽  
Covariance Operators

Abstract This paper is the continuation of [Vakhania and Kandelaki, Teoriya Veroyatnost. i Primenen 41: 31–52, 1996] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra.

Robust kernel canonical correlation analysis to detect gene-gene co-associations: A case study in genetics

2019 ◽  
Vol 17 (04) ◽  
pp. 1950028 ◽  
Author(s):  
Md. Ashad Alam ◽  
Osamu Komori ◽  
Hong-Wen Deng ◽  
Vince D. Calhoun ◽  
Yu-Ping Wang
Keyword(s):  
Correlation Analysis ◽  
Canonical Correlation Analysis ◽  
Canonical Correlation ◽  
Enrichment Analysis ◽  
Superior Performance ◽  
Covariance Operator ◽  
Contaminated Data ◽  
Cross Covariance ◽  
Kernel Canonical Correlation Analysis ◽  
Kernel Cca

The kernel canonical correlation analysis based U-statistic (KCCU) is being used to detect nonlinear gene–gene co-associations. Estimating the variance of the KCCU is however computationally intensive. In addition, the kernel canonical correlation analysis (kernel CCA) is not robust to contaminated data. Using a robust kernel mean element and a robust kernel (cross)-covariance operator potentially enables the use of a robust kernel CCA, which is studied in this paper. We first propose an influence function-based estimator for the variance of the KCCU. We then present a non-parametric robust KCCU, which is designed for dealing with contaminated data. The robust KCCU is less sensitive to noise than KCCU. We investigate the proposed method using both synthesized and real data from the Mind Clinical Imaging Consortium (MCIC). We show through simulation studies that the power of the proposed methods is a monotonically increasing function of sample size, and the robust test statistics bring incremental gains in power. To demonstrate the advantage of the robust kernel CCA, we study MCIC data among 22,442 candidate Schizophrenia genes for gene–gene co-associations. We select 768 genes with strong evidence for shedding light on gene–gene interaction networks for Schizophrenia. By performing gene ontology enrichment analysis, pathway analysis, gene–gene network and other studies, the proposed robust methods can find undiscovered genes in addition to significant gene pairs, and demonstrate superior performance over several of current approaches.

scholarly journals Scaling laws and warning signs for bifurcations of SPDEs

2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO
Keyword(s):  
Differential Equations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Warning Signs ◽  
Covariance Operator ◽  
Large Classes ◽  
Practical Applications ◽  
Critical Transitions ◽  
Degenerate Eigenvalues ◽  
Adjoint Operators

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

scholarly journals The Topological Support of Gaussian Measure in Banach Space

1975 ◽  
Vol 57 ◽  
pp. 59-63 ◽  
Author(s):  
N. N. Vakhania
Keyword(s):  
Banach Space ◽  
Probability Measure ◽  
Gaussian Measure ◽  
Separable Banach Space ◽  
Covariance Operator ◽  
Probability Measures ◽  
Gaussian Measures ◽  
Linear Spaces

The main result of the present paper is the theorem 1, which describes the topological support of an arbitrary Gaussian measure in a separable Banach space. This theorem will be proved after some discussion of the notion of support itself. But we begin with the reminder of the notion of covariance operator of a probability measure. This notion has a great importance not only for the description of support of Gaussian measures but also for the study of other problems in the theory of probability measures in linear spaces (c.f. [1], [2]).

scholarly journals Generalized partially functional linear model

2021 ◽  
Author(s):  
Weiwei Xiao ◽  
Yixuan Wang ◽  
Haiyan Liu
Keyword(s):  
Mortality Rate ◽  
Sleep Quality ◽  
Sleep Onset ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Regression Coefficients ◽  
Covariance Operator ◽  
Functional Linear Model ◽  
True Value ◽  
Functional Linear Regression

Abstract In this paper, we propose a generalized functional linear regression model with scalar and functional multiple predictors. We develop maximum likelihood estimators for the regression coefficients. For the functional predictors, we adopt the method of functional principal component analysis to reduce their dimensions. We then propose the generalized auto-covariance operator, based on which an appropriate measure quantifies the difference between the estimators and their true values is established. The asymptotic joint distribution of estimated regression functions is proved. For the scalar predictors, we establish a distance between the estimated value and the true value, and prove the asymptotic property of the estimated regression coefficients. Extensive simulation experiment results are consistent with the theoretical result. Finally, two application examples of the model are given. One is sleep quality study where we studied the effects of heart rate, percentage of sleep time on total sleep in bed, wake after sleep onset and number of wakening during the night on sleep quality in 22 healthy people. The other one is mortality rate where we studied the effects of air quality index, temperature, relative humidity , GDP per capita and the number of beds per thousand people on the mortality rate across 80 major cities in China.

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