A Comparison of Some Methods for the Selection of a Common Eigenvector Model for the Covariance Matrices of Two Groups

Pepler, P.T.; Uys, D. W.; Nel, Daan

doi:10.1080/03610918.2014.932801

Cited by 9 publications

(16 citation statements)

References 16 publications

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“…For the normally distributed data, the normalization process (5.2) is skipped and W g = X g 1/2 g . For a sufficiently large sample size the covariance matrix of W g is approximately g (Pepler, Uys, and Nel 2016). The underlying common eigenvectors ( ) are obtained from = A A/8 where A : 8× p is simulated from a multivariate normal distribution with a zero mean and with an identity covariance matrix.…”

Section: Simulation Studymentioning

confidence: 99%

“…To identify an appropriate common eigenvector model for the data, two goodnessof-fit measurements were proposed by Flury (1988): a log-likelihood ratio (LR) statistic and the Akaike information criterion (AIC). Pepler, Uys, and Nel (2016) compared 8 methods for selecting suitable common eigenvector models, including the LR statistic and AIC. This article considers three model identification methods: the AIC, the Schwarz criterion [also known as the Bayesian information criterion (BIC)], and the LR statistic, to be used to identify an appropriate model for a given dataset.…”

Section: Introductionmentioning

confidence: 99%

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A comparison of two estimation methods for common principal components

Duras

2019

Communications in Statistics: Case Studies, Data Analysis and A

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Common principal components (CPCs) are often estimated using maximum likelihood estimation through an algorithm called the Flury-Gautschi (FG) Algorithm. Krzanowski proposed a simpler estimation method via a principal component analysis of a weighted sum of the sample covariance matrices. These methods are compared for real-world datasets and in a Monte Carlo simulation. The real-world data is used to compare the selection of a common eigenvector model and the estimated coefficients. The simulation study investigates how the accuracy of the methods is affected by autocorrelation, the number of covariance matrices, dimensions, and sample sizes for multivariate normal and chi-square distributed data. The findings in this article support the use of Krzanowski's method in situations where the CPC assumption is appropriate. ARTICLE HISTORY

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Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A comparison of two estimation methods for common principal components

Duras

2019

Communications in Statistics: Case Studies, Data Analysis and A

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“…To the best of our knowledge, we are the first to provide asymptotic results as the number of matrices goes to infinity. Different from the literature where n is fixed (Flury, 1987;Boik, 2002;Pepler et al, 2016;Wang et al, 2019), Assumptions A (2) and (3) assume (λ i1 , . .…”

Section: Model and Assumptionsmentioning

confidence: 99%

“…Among these extensions of CPCA, PCPCA continues to be appealing, as it relaxes the assumption of a completely common eigenspace across matrices while partially preserving the straightforward interpretation of common eigenvectors, i.e., eigenvectors shared across matrices. Related work on this topic includes Krzanowski (1984), Schott (1999), Boik (2002), Lock et al (2013) and Pepler et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Partial Common Principal Component Analysis for Covariance Matrices

Wang

Luo

Zhao

et al. 2019

Preprint

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We consider the problem of jointly modeling multiple covariance matrices by partial common principal component analysis (PCPCA), which assumes a proportion of eigenvectors to be shared across covariance matrices and the rest to be individual specific. This paper proposes consistent estimators of shared eigenvectors (called CPCs) in PCPCA as the number of matrices or the number of samples to estimate each matrix goes to infinity. We prove such asymptotic results without making any assumptions on the ranks of the CPC-related eigenvalues. When the number of samples goes to infinity, our result does not require the data to be Gaussian distributed. Furthermore, this paper introduces a sequential testing procedure to identify the number of shared eigenvectors in PCPCA. In simulation studies, our method shows higher accuracy in estimating CPCs than competing methods. Applied to a motor-task functional magnetic resonance imaging data set, our estimator identifies meaningful brain networks that are consistent with current scientific understandings.

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“…The Durbin-Watson test was used to test for autocorrelation. The Durbin-Watson statistic was computed following Equation (18).…”

Section: Stationarity Of Extended Time Seriesmentioning

confidence: 99%

Infilling Monthly Rain Gauge Data Gaps with Satellite Estimates for ASAL of Kenya

et al. 2016

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Design and operation of water resources management systems in sub-Saharan Africa suffer from inadequate observation data. Long running uninterrupted time series of data are often not available for water resource planning. Incomplete datasets with missing gaps is a challenge for users of the data. Inadequate data compromise results of analyses leading to wrong inference and conclusions of scientific assessments and research. Infilling of missing sections of data is necessary prior to the practical use of hydrometeorological time series. This paper proposes the use of Tropical Rainfall Measuring Mission satellite data as a viable alternate source of infill for missing rain gauge records. The least square regression method, using satellite-based estimates of rainfall was tested to fill in the missing data for 153 data points at nine rain gauge stations in Machakos, Makueni and the Kitui region of Kenya. Results suggest that the satellite rainfall estimates can be used as an alternative data source for rainfall series where the missing data gaps are large. The infilled data series were used in the development of monitoring, forecasting and drought early warning for Arid and Semi-Arid Lands (ASAL) in Kenya.

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A Comparison of Some Methods for the Selection of a Common Eigenvector Model for the Covariance Matrices of Two Groups

Cited by 9 publications

References 16 publications

A comparison of two estimation methods for common principal components

A comparison of two estimation methods for common principal components

Semiparametric Partial Common Principal Component Analysis for Covariance Matrices

Infilling Monthly Rain Gauge Data Gaps with Satellite Estimates for ASAL of Kenya

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