• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.895-907
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• 2003

Recent demands for representing the location of multivariate data produce various multivariate medians such as Tukey median, Oja median and spatial median. They are considered as multivariate versions of the median which is widely recognized as a robust alternative to the arithmetic mean. Many studies show that those multivariate median preserve the robustness. However, the effectiveness of those medians is not fully identified. In this note the relative efficiencies of the multivariate medians are investigated in various configurations under the bivariate t-distribution. It is shown that Tukey median outperforms the others in most configurations.

• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.1-13
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• 2018

In many studies, a researcher attempts to describe a population where units are measured for multiple outcomes, or responses. In this paper, we present an efficient procedure based on ranked set sampling to estimate and perform hypothesis testing on a multivariate mean. The method is based on ranking on an auxiliary covariate, which is assumed to be correlated with the multivariate response, in order to improve the efficiency of the estimation. We showed that the proposed estimators developed under this sampling scheme are unbiased, have smaller variance in the multivariate sense, and are asymptotically Gaussian. We also demonstrated that the efficiency of multivariate regression estimator can be improved by using Ranked set sampling. A bootstrap routine is developed in the statistical software R to perform inference when the sample size is small. We use a simulation study to investigate the performance of the method under known conditions and apply the method to the biomarker data collected in China Health and Nutrition Survey (CHNS 2009) data.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• Journal of Preventive Medicine and Public Health
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• 제31권4호
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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.

• Communications for Statistical Applications and Methods
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• 제23권6호
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• pp.497-515
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• 2016

Modern processes often monitor more than one quality characteristic that are referred to as multivariate statistical process control (MSPC) procedures. The MSPC is the most rapidly developing sector of statistical process control and increases interest in the simultaneous inspection of several related quality characteristics. Most multivariate detection procedures based on a multi-normality assumptions are independent, but there are many processes that assume non-normality and correlation. Many multivariate control charts have a lack of related joint distribution. Copulas are tool to construct multivariate modelling and formalizing the dependence structure between random variables and applied in several fields. From copula literature review, there are a few copula to apply in MSPC that have multivariate control charts, and represent a successful tool to identify an out-of-control process. This paper presents various types of copulas modelling for the multivariate control chart. The performance measures of the control chart are the average run length (ARL) and the average number of observations to signal (ANOS). Furthermore, a Monte Carlo simulation is shown when the observations were from an exponential distribution.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.939-946
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• 1999

We propose methods for detecting influential observations that have a large influence on the likelihood ratio test statistic for the multivariate Behrens-Fisher problem. For this purpose we derive the influence curve and the derivative influence of the likelihood ratio test statistic. An illustrative example is given to show the effectiveness of the proposed methods on the identification of influential observations.

• 응용통계연구
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• 제13권2호
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• pp.383-392
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• 2000

1970년대 후반부터 영향력이 있는 관측값을 검출하기 위해서 회귀분석을 포함한 다양한 다변량 해석법에서의 영향분석 및 감도분석에 대한 연구가 진행되어 왔다. 결손 값이 포함된 불완전한 자료에 관해서도 이러한 연구가 필요하다. 이와 관련하여 Kim et al.(1998)등은 평균벡터와 분산공분산행렬에 대한 최우추정값에 초점을 두고 불완전한 자료에 대한 다변량 해석법에서의 감도분석에 관한 방법적 연구를 다루었다. Kim et al.(1998)에서는 Cook’s D 통계량을 이용하였으나, 본 논문에서는 결손값이 있는 다변량 자료에 대해서 주성분을 이용하여 영향력이 있는 관측값을 검출하는 방법에 대해서 살펴보았다. 이 때, 결손값은 EM알고리즘에 의해 대치하여 PCA 통계량을 유도하였다.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.507-514
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• 2001

In recent years, the development and the embodiment of information analysis system has been sprightly carried out in several fields of study. In this study, as and extension of these studies, we develop a system for multivariate analysis which might be widely used in social and natural sciences. This multivariate analysis system is developed by using multivariate analysis procedures in SAS/STAT software. Also, the system supply users with he environment of GUI(Graphical User Interface), which is constructed with AF(application frame) and SCL(screen control language) of SAS software, in order to help users to use the system with easy.

• Communications for Statistical Applications and Methods
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• 제25권2호
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• pp.109-130
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• 2018

Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.613-635
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• 2001

This paper proposes a skewed multivariate probit model for analyzing a correlated binary response data with covariates. The proposed model is formulated by introducing an asymmetric link based upon a skewed multivariate normal distribution. The model connected to the asymmetric multivariate link, allows for flexible modeling of the correlation structure among binary responses and straightforward interpretation of the parameters. However, complex likelihood function of the model prevents us from fitting and analyzing the model analytically. Simulation-based Bayesian inference methodologies are provided to overcome the problem. We examine the suggested methods through two data sets in order to demonstrate their performances.