• Journal of Preventive Medicine and Public Health
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• v.31 no.4 s.63
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• pp.875-884
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• 1998

Missing observations are common in medical research and health survey research. Several statistical methods to handle the missing data problem have been proposed. The EM algorithm (Expectation-Maximization algorithm) is one of the ways of efficiently handling the missing data problem based on sufficient statistics. In this paper, we developed statistical models and methods for survey data with multivariate missing observations. Especially, we adopted the EM algorithm to handle the multivariate missing observations. We assume that the multivariate observations follow a multivariate normal distribution, where the mean vector and the covariance matrix are primarily of interest. We applied the proposed statistical method to analyze data from a health survey. The data set we used came from a physician survey on Resource-Based Relative Value Scale(RBRVS). In addition to the EM algorithm, we applied the complete case analysis, which uses only completely observed cases, and the available case analysis, which utilizes all available information. The residual and normal probability plots were evaluated to access the assumption of normality. We found that the residual sum of squares from the EM algorithm was smaller than those of the complete-case and the available-case analyses.

• Journal of Korea Water Resources Association
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• v.30 no.2
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• pp.155-163
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• 1997

In this study, drought analysis of annual flows of Jindong, Hyunpoong, and Waekwan stations located at Nakdong River Basins was performed based on multivariate stochastic models. The stochastic models used were multivariate autoregressive model (MAR) and multivariate contemporaneous (MCAR) model. MCAR(1) and MAR(1) models were selected to be a appropriate models for these stations based on skewness test of normality, test of uncorrelated residuals, and correlograms of the residual series of each model. The statistics generated by MCAR(1) model and MAR(1) model resembled very closely those computed from historical series. The drought characteristics such as run len호, run sum, and run intensity were fairly well reproduced for the various lengths of generated annual flows based on the MCAR(1) and MAR(1) models. Thus, these drought characteristics may give the important informations in planning mid or long term water supplying systems.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.479-485
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• 2003

The influence of observations on the Wilks' lambda test of a linear hypothesis in multivariate regression is investigated using the local influence method. The perturbation scheme of case-weights is considered. A numerical example is given to show the effectiveness of the local influence method in identifying the influential observations.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.243-248
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• 1995

The problem of optimal design for a nonparametric regression with binary data is considered. The aim of the statistical analysis is the estimation of a quantal response surface in two dimensions. Bias, variance and IMSE of kernel estimates are derived. The optimal design density with respect to asymptotic IMSE is constructed.

• Food Science and Preservation
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• v.30 no.4
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• pp.573-588
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• 2023

The purpose of this study was to monitor changes in the quality of ginseng and predict its shelf-life. As the storage period of ginseng increased, some quality indicators, such as water-soluble pectin (WSP), CDTA-soluble pectin (CSP), cellulose, weight loss, and microbial growth increased, while others (Na₂CO₃-soluble pectin/NSP, hemicellulose, starch, and firmness) decreased. Principal component analysis (PCA) was performed using the quality attribute data and the principal component 1 (PC1) scores extracted from the PCA results were applied to the multivariate analysis. The reaction rate at different temperatures and the temperature dependence of the reaction rate were determined using kinetic and Arrhenius models, respectively. Among the kinetic models, zeroth-order models with cellulose and a PC1 score provided an adequate fit for reaction rate estimation. Hence, the prediction model was constructed by applying the cellulose and PC1 scores to the zeroth-order kinetic and Arrhenius models. The prediction model with PC1 score showed higher R² values (0.877-0.919) than those of cellulose (0.797-0.863), indicating that multivariate analysis using PC1 score is more accurate for the shelf-life prediction of ginseng. The predicted shelf-life using the multivariate accelerated shelf-life test at 5, 20, and 35℃ was 40, 16, and 7 days, respectively.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.679-688
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• 2008

In multivariate regression analysis there exist many influence measures on the regression estimates. However it seems to be few of influence diagnostics on test statistics in hypothesis testing. Case-deletion approach is fundamental for investigating influence of observations on estimates or statistics. Tang and Fung (1997) derived single case-deletion of the Wilks' ratio, Lawley-Hotelling trace, Pillai's trace for testing a general linear hypothesis of the regression coefficients in multivariate regression. In this paper we derived more extended form of those measures to deal with joint influence among observations. A numerical example is given to illustrate the effect of joint influence on the test statistics.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.641-649
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• 2017

Multivariate confidence regions were defined using a chi-square distribution function under a normal assumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be obtained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.

• Nuclear Engineering and Technology
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• v.51 no.1
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• pp.45-53
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• 2019

Thermal-hydraulic passive safety systems (PSSs) are incorporated into many advanced reactor designs on the bases of simplicity, economics and inherent safety nature. Several factors among which are the critical parameters (CPs) that influence failure and reliability of thermal-hydraulic (t-h) passive systems are now being explored. For simplicity, it is assumed in most reliability analyses that the CPs are independent whereas in practice this assumption is not always valid. There is need to critically examine the dependency influence of the CPs on reliability of the t-h passive systems at design stage and in operation to guarantee safety/better performance. In this paper, two multivariate analysis methods (covariance and conditional subjective probability density function) were presented and applied to a simple PSS. The methods followed a generalized procedure for evaluating t-h reliability based on dependency consideration. A passively water-cooled steam generator was used to demonstrate the dependency of the identified key CPs using the methods. The results obtained from the methods are in agreement and justified the need to consider the dependency of CPs in t-h reliability. For dependable t-h reliability, it is advisable to adopt all possible CPs and apply suitable multivariate method in dependency consideration of CPs among other factors.

• International Journal of Human Ecology
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• v.14 no.1
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• pp.29-39
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• 2013

The study examined how changes in time invested in private tutoring and academic achievement influenced each other through a multivariate latent growth model by using the data from the first to the third year presented in the KYPS. This study identifies not only how changes in the private tutoring experience exerted a direct influence on changes in academic achievement, but also measures what kind of changes in private tutoring and academic achievement had emerged over time. The detailed study results are as follows. First, the analysis of time invested in private tutoring showed that the higher the grades, the greater were the amount of time invested in private tutoring in the case of Korean language study. On the other hand, the results showed that in the case of English and mathematics, the higher the grades, the lesser was the amount of time invested in private tutoring. Second, private tutoring and academic achievement were all in a linear relationship. Third, it was shown that the time invested in private tutoring and academic achievement exerted a negative influence on each other according to the passage of time.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.3
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• pp.289-296
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• 2001

This paper proposes multivariate control chart for autocorrelated data which are common in chemical and process industries and lead to increase in the number of false alarms when conventional control charts are applied. The effect of autocorrelated data is modeled as a vector autoregressive process, and canonical analysis is used to reduce the dimensionality of the data set and find the canonical variables that explain as much of the data variation as possible. Charting statistics are constructed based on the residual vectors from the canonical variables which are uncorrelated over time, and therefore the control charts for these statistics can attenuate the autocorrelation in the process data. The charting procedures are illustrated with a numerical example and Monte Carlo simulation is conducted to investigate the performances of the proposed control charts.