A novel definition of the multivariate coefficient of variation

Albert, Adelin; Zhang, Lixin

doi:10.1002/bimj.201000030

Cited by 73 publications

(59 citation statements)

References 17 publications

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“…Coefficient of variation (CV), the ratio of standard deviation to the mean, was calculated to assess the amount of dispersion and precision by which parameters were measured. 1 All analyses were performed using SAS for Windows (version 9.2, SAS Institute).…”

Section: Discussionmentioning

confidence: 99%

Estimation of normal computed tomography measurements for the upper cervical spine in the pediatric age group

Vachhrajani

Sen

Satyan

et al. 2014

PED

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Object Upper cervical spine injuries in the pediatric age group have been recognized as extremely unstable from ligamentous disruption and as potentially lethal. Few measurement norms have been published for the pediatric upper cervical spine to help diagnose this pathological state. Instead, adult measurement techniques and results are usually applied inappropriately to children. The authors propose using high-resolution reconstructed CT scans to define a range of normal for a collection of selected upper cervical spine measurements in the pediatric age group. Methods Sagittal and coronal reformatted images were obtained from thin axial CT scans obtained in 42 children (< 18 years) in a 2-month period. There were 25 boys and 17 girls. The mean age was 100.9 months (range 1–214 months). Six CT scans were obtained for nontrauma indications, and 36 were obtained as part of a trauma protocol and later cleared for cervical spine injury. Six straightforward and direct linear distances—basion-dental interval (BDI); atlantodental interval (ADI); posterior atlantodental interval (PADI); right and left lateral mass interval (LMI); right and left craniocervical interval (CCI); and prevertebral soft-tissue thickness at C-2—that minimized logistical and technical distortions were measured and recorded. Statistical analysis including interobserver agreement, age stratification, and sex differences was performed for each of the 6 measurements. Results The mean ADI was 2.25 ± 0.24 mm (± SD), the mean PADI was 18.3 ± 0.07 mm, the mean BDI was 7.28 ± 0.10 mm, and the mean prevertebral soft tissue width at C-2 was 4.45 ± 0.43 mm. The overall mean CCI was 2.38 ± 0.44 mm, and the overall mean LMI was 2.91 ± 0.49 mm. Linear regression analysis demonstrated statistically significant age effects for PADI (increased 0.02 mm/month), BDI (decreased 0.02 mm/month), and CCI (decreased 0.01 mm/month). Similarly significant effects were found for sex; females demonstrated on average a smaller CCI by 0.26 mm and a smaller PADI by 2.12 mm. Moderate to high interrater reliability was demonstrated across all parameters. Conclusions Age-dependent and age-independent normal CT measurements of the upper cervical spine will help to differentiate physiological and pathological states in children. The BDI appears to change significantly with age but not sex; on the other hand, the LMI and ADI appear to be age-independent measures. This preliminary study suggests acceptable levels of interrater reliability, and further expanded study will aim to validate these measurements to produce a profile of normal upper cervical spine measurements in children.

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Section: Discussionmentioning

confidence: 99%

Estimation of normal computed tomography measurements for the upper cervical spine in the pediatric age group

Vachhrajani

Sen

Satyan

et al. 2014

PED

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“…For p = 1, Sokal and Brauman [18] already reported that the classical estimator of the CV is negatively 245 biased. In the multivariate context, Zhang [24] also empirically noticed the fact that the classical estimators of the multivariate coefficients of variation that Albert and Zhang [2] considered were all biased under normality.…”

Section: Bias Of the Classical Estimator Of Voinov And Nikulin's MCVmentioning

confidence: 99%

“…For instance, in biology, Van Valen [21] noticed the inadequacy of the univariate CV when dealing with skeletal measurements on mammals. In the context of EQA analyses, Albert and Zhang [2] and Zhang et al [25] also pointed out this particular issue. Another common approach consists in averaging the marginal CV's to obtain an index of global relative dispersion (as in [3]).…”

Section: Introductionmentioning

confidence: 99%

“…However, as it is not easy to compare p × p matrices, the aim of this paper is to further develop the theory related to multivariate 25 extensions of the coefficient of variation (MCV) that summarize multivariate relative variability in one single index. Several propositions have already been introduced in the literature (see [2] for a review). In this paper, focus will be on Voinov and Nikulin's MCV [23], which is a distance-based measure defined by the inverse of the square root of the Mahalanobis distance between the (non-null) mean vector and the origin of the design space, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…As a reminder, V n denotes the classical estimator, while V 1 n uses an unbiased estimator of γ −2 under normality. All other estimators, based on the same principle, use an estimator of the bias obtained from the expectation-curve under normality forV (2) n , by jackknife forV (3) n , by bootstrap forV (4) n and by inversion of the expectation-curve under normality forV (5) n . We can observe that all the obtained 345 corrected estimates are indeed higher than the classical estimates.…”

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confidence: 99%

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Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation

2016

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In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distancebased multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations.

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Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

Nguyen¹,

Tran

Heuchenne

et al. 2019

Appl Stoch Models Bus & Ind

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In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.

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A novel definition of the multivariate coefficient of variation

Cited by 73 publications

References 17 publications

Estimation of normal computed tomography measurements for the upper cervical spine in the pediatric age group

Estimation of normal computed tomography measurements for the upper cervical spine in the pediatric age group

Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

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