Regularized covariance matrix estimation under the common principal components model

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

doi:10.1080/03610918.2015.1040499

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Initial methods include principal component analysis (PCA) [5] and factor models [6]. Other prevalent techniques encompass the constant correlation approach [7], maximum likelihood estimation (MLE) [8], shrinkage methods [9,10], and so on [11]. Notably, shrinkage methods have demonstrated exceptional efficacy in financial portfolio allocation.…”

Section: Introductionmentioning

confidence: 99%

Element Aggregation for Estimation of High-Dimensional Covariance Matrices

Yang

2024

Mathematics

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This study addresses the challenge of estimating high-dimensional covariance matrices in financial markets, where traditional sparsity assumptions often fail due to the interdependence of stock returns across sectors. We present an innovative element-aggregation method that aggregates matrix entries to estimate covariance matrices. This method is designed to be applicable to both sparse and non-sparse matrices, transcending the limitations of sparsity-based approaches. The computational simplicity of the method’s implementation ensures low complexity, making it a practical tool for real-world applications. Theoretical analysis then confirms the method’s consistency and effectiveness with its convergence rate in specific scenarios. Additionally, numerical experiments validate the method’s superior algorithmic performance compared to conventional methods, as well as the reduction in relative estimation errors. Furthermore, empirical studies in financial portfolio optimization demonstrate the method’s significant risk management benefits, particularly its ability to effectively mitigate portfolio risk even with limited sample sizes.

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Section: Introductionmentioning

confidence: 99%

Element Aggregation for Estimation of High-Dimensional Covariance Matrices

Yang

2024

Mathematics

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“…When selecting a model from Flury's hierarchy, several methods can be used for nonnormal data. For example, the bootstrap hypothesis test (BootTest) of Klingenberg (1996), random vector correlation (RVC) of Klingenberg and McIntyre (1998), and bootstrap vector correlation distribution (BVD), bootstrap confidence regions (BCR), and the ensemble method of Pepler (2014). The ensemble method determines the majority vote on commonness from the AIC, RVC, BootTest, BVD, and BCR methods.…”

Section: Introductionmentioning

confidence: 99%

Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure

Kim

Park

2022

Environmetrics

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Spatiotemporal measurements observed through river networks have two distinct characteristics: a spatiotemporal correlation under the flow‐connected structure and the existence of heterogeneous covariances, which require a careful approach to implement principal component analysis (PCA). This paper focuses on developing a PCA method to reflect the unique characteristics of river networks. We propose a novel method combining flow‐directed PCA and geographically weighted PCA for the domain of river networks. The strengths of our approach are that it can (i) reduce dimensionality for streamflow data while effectively removing correlation among them and (ii) identify the group structure of data. It is possible to find essential patterns and sources of variation that may not be disclosed due to the attributes of flow‐connected networks. We apply the proposed method to the daily monitoring records of total organic carbon in the Geum River catchment area in South Korea. The results show that the proposed method successfully adjusts for the topological structure of the network and temporal correlation among observations while considering the spatial heterogeneity, enabling a more concrete understanding of monitoring networks.

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Discriminant analysis under the common principal components model

Pepler

Uys

Nel

2017

Communications in Statistics - Simulation and Computation

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For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularised CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations where the CPC model is applicable. This paper extends their work to the context of discriminant analysis for two groups, by plugging the regularised CPC estimator into the ordinary quadratic discriminant function.Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures.

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Regularized covariance matrix estimation under the common principal components model

Cited by 3 publications

References 15 publications

Element Aggregation for Estimation of High-Dimensional Covariance Matrices

Element Aggregation for Estimation of High-Dimensional Covariance Matrices

Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure

Discriminant analysis under the common principal components model

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