Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues

Fan, Jinyu; Shu, Lianjie; Yang, Aijun; Li, Yanting

doi:10.1080/00224065.2020.1746212

Cited by 16 publications

(4 citation statements)

References 31 publications

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“…In this subsection, we provide another example using a multivariate dataset of diagnostic breast cancer. The dataset is available through the ftp server in the Computer Sciences Department at UW-Madison: http://ftp.cs.wisc.edu/ math-prog/cpo-dataset/machine-learn/cancer/WDBC/ and has been recently used by Fan et al (2021) for detecting change in Phase I of the high-dimensional covariance matrix. This dataset consists of 567 vector observations, and for each observation, there are 30 real-valued features/variables measured for each observation, as well as a categorical as Phase-I out-of-control observations and trying to detect whether there is a shift in the mean between these two types.…”

Section: An Example Of Diagnostic Breast Cancer Datasetmentioning

confidence: 99%

Phase I Analysis of High-Dimensional Multivariate Processes in the Presence of Outliers

Ebadi¹,

Chenouri²,

Steiner³

2021

Preprint

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One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of highdimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I in terms of the probability of signal criterion. This assessment is carried out in the absence and presence of outliers. We show that, in both phases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

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Section: An Example Of Diagnostic Breast Cancer Datasetmentioning

confidence: 99%

Phase I Analysis of High-Dimensional Multivariate Processes in the Presence of Outliers

Ebadi¹,

Chenouri²,

Steiner³

2021

Preprint

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“…However the Phase I monitoring of high-dimensional process is rarely discussed. One exception is Fan et al (2021) who studied Phase I analysis of the high-dimensional covariance matrix by tracking changes in the sparse leading eigenvalue of two sample covariance matrices. This article focuses on Phase I monitoring of mean changes in high-dimensional process.…”

Section: Introductionmentioning

confidence: 99%

A phase I change‐point method for high‐dimensional process with sparse mean shifts

Huang

Shu²,

et al. 2023

Naval Research Logistics

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Although Phase I analysis of multivariate processes has been extensively discussed, the discussion on techniques for Phase I monitoring of high-dimensional processes is still limited. In high-dimensional applications, it is common to observe that a large number of components but only a limited number of them change at the same time. The shifted components are often sparse and unknown a priori in practice. Motivated by this, this article studies Phase I monitoring of high-dimensional process mean vectors under an unknown sparsity level of shifts. The basic idea of the proposed monitoring scheme is to first employ the false discovery rate procedure to estimate the sparsity level of mean shifts, and then to monitor the mean changes based on the maximum of the directional likelihood ratio statistics over all the possible shift directions. The comparison results based on extensive simulations favor the proposed monitoring scheme. A real example is presented to illustrate the implementation of the new monitoring scheme.

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“…They used simulated and real-life examples to investigate the sensitivity of their 3 suggested chart, named as T-COV, in terms of signal probability metric. Taking the idea of tracking changes in the sparse leading eigenvalue between two covariance matrices, Fan et al [13] designed a sparse-leading-eigenvalue-driven control chart for Phase I monitoring of highdimensional process variability. They showed that their proposed control chart works better than L 2 -type and L  -type control charts.…”

Section: Introductionmentioning

confidence: 99%

A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

2022

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Online monitoring of high-dimensional processes variability in which the number of variables is larger than the sample size is a challenging issue for quality practitioners because the sample covariance matrix is not invariable. To deal with this challenge, a generalized multiple dependent state sampling (GMDS) chart based on ridge penalized likelihood ratio (RPLR) statistic is developed for Phase II monitoring of multivariate process variability under high-dimensional setting. The developed control chart benefits from three advantages: (1) departing from the conventional covariance matrix charts, it can be efficiently employed for both spars and nonspars covariance matrices; (2) it is able to detect spars shift patterns in which only a few covariance matrix elements are deviated from their nominal values; and (3) it outperforms the detectability of the RPLR chart in terms of average run length (ARL) and standard deviation of run length (SDRL). The performance of RPLR, MDS-RPLR, and GMDS-RPLR charts are compared using extensive simulation studies by considering different diagonal and/or offdiagonal covariance matrix disturbances. Moreover, sensitivity analysis are provided to analyze how the number of process variables and GMDS parameter affect the run length properties of the developed chart.

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Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues

Cited by 16 publications

References 31 publications

Phase I Analysis of High-Dimensional Multivariate Processes in the Presence of Outliers

Phase I Analysis of High-Dimensional Multivariate Processes in the Presence of Outliers

A phase I change‐point method for high‐dimensional process with sparse mean shifts

A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

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