• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.187-191
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• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under a non-normal distribution.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.875-883
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• 2001

We derive the asymptotic relative efficiencies in two special cases of Chaudhuri's estimators for the multivariate one sample problem. And we compare those two when observations are independent and identically distributed from a family of spherically symmetric distributions including normal distributions.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.33-40
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• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.27 no.2
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• pp.113-124
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• 2024

Purpose: Alarm symptoms (red flag signs) are crucial indications for management decisions on pediatric gastrointestinal endoscopy. We aimed to identify items in the alarm symptoms and pre-endoscopic investigations that predict abnormal endoscopy results. Methods: A retrospective descriptive study was conducted among children aged under 18 years undergoing endoscopy. The patients were classified into normal and abnormal endoscopic groups. The incidence of alarm symptoms and pre-endoscopic investigations were compared between the groups. Univariate and multivariate logistic regression analyses were performed to determine independent risk factors for abnormal endoscopy. Results: Of 148 participants, 66 were classified in the abnormal endoscopy group. Compared with the normal group, the abnormal group had a significantly higher prevalence of alarm symptoms. Moreover, hematemesis/hematochezia, anemia, low hemoglobin level, hypoalbuminemia, rising erythrocyte sedimentation rate, increased serum lipase, and blood urea nitrogen/creatinine ratio were significantly higher in the abnormal endoscopy group than in the normal group. Multivariate logistic regression analysis indicated that hematemesis/hematochezia and low hemoglobin level were independent risk factors for abnormal endoscopy. Conclusion: The alarm symptoms and pre-endoscopic investigations were evaluated using predictive factors for abnormal pediatric endoscopic findings. According to multivariate logistic regression analysis, hematemesis/hematochezia and low hemoglobin levels were independent risk factors for abnormal endoscopy.

• Journal of Integrative Natural Science
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• v.5 no.4
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• pp.246-252
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• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.1027-1034
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. When the joint distribution of the process variables is multivariate normal, multivariate Shewhart control charts using the function of the maximum likelihood estimator for monitoring the dispersion matrix are considered for the simultaneous monitoring of the dispersion matrix. The performances of the multivariate Shewhart control charts based on the proposed control statistic are evaluated in term of average run length (ARL). The performance is investigated in three cases, where the variances, covariances, and variances and covariances are changed respectively. The numerical results show that the performances of the proposed multivariate Shewhart control charts are not better than the control charts using the trace of the covariance matrix in the Jeong and Cho (2012) in terms of the ARLs.

• Proceedings of the Safety Management and Science Conference
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• 2005.05a
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• pp.503-521
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• 2005

Process capability indices are widely used in industries and quality assurance system. When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in considertion of the correlations among the characteristics. To solve the issue on the optimal design for muliple quality characteristics, the study propose the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of terms. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^{++}$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other,

• Proceedings of the Safety Management and Science Conference
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• 2004.11a
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• pp.69-79
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• 2004

Process capability indices are widely used in industries and quality assurance system. When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in considertion of the correlations among the characteristics. To solve the issue on the optimal design for multiple quality characteristics, the study propose the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of terms. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^{++}$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.807-814
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• 2012

We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.