• 응용통계연구
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• 제25권4호
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• pp.605-612
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• 2012

Multivariate data are often generated with multiple outcomes in various fields. Multiple outcomes could be mixed as continuous and discrete. Because of their complexity, the data are often dealt with by separately applying regression analysis to each outcome even though they are associated the each other. This univariate approach results in the low efficiency of estimates for parameters. We study the efficiency gains of the multivariate approaches relative to the univariate approach with the mixed data that include continuous and binary outcomes. All approaches yield consistent estimates for parameters with complete data. By jointly estimating parameters using multivariate methods, it is generally possible to obtain more accurate estimates for parameters than by a univariate approach. The association between continuous and binary outcomes creates a gap in efficiency between multivariate and univariate approaches. We provide a guidance to analyze the mixed data.

• Communications for Statistical Applications and Methods
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• 제2권1호
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• pp.201-208
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• 1995

In the last years there has been growing interest in concepts of positive dependence for families of random variables such that concepts are considerable us in deriving inequalities in probability and statistics. Lehman introdued various concepts of positive dependence for bivariate random variables. A much stronger notions of positive dependence were later considered by Esary, Proschan, and Walkup. Ahmed et al and Ebrahimi and Ghosh also obtained multivariate versions of various bivariate positive dependence as descrived by Lehman. See also Block al. Glaz and Johnson an Barlow and Proschan and the references there. Multivariate processes arise when instead of observing a single process we observe several processes, say $X_19t), \cdots, X_n(t)$ simultaneously. For example, in an engineering context we may want to study the simultaneous variation of current and voltage, or temperature, pressure and volume over time. In economics we may be interested in studying inflation rates and money supply, unemployment and interest rates. We could of course, study each quantity on its own and treat each as a separate univariate process. Although this would give us some information about each quantity it could never give information about the interrelationship between various quantities. This leads us to introduce some concepts of positive and for multivariate stochastic processes. The concepts of positive dependence have subsequently been extended to stochastic processes in different directions by many authors.

• Communications for Statistical Applications and Methods
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• 제24권6호
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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.

• Communications for Statistical Applications and Methods
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• 제27권2호
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• pp.255-268
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• 2020

A mixture of multivariate canonical fundamental skew t-distribution (CFUST) has been of interest in various fields. In particular, interest in the unsupervised learning society is noteworthy. However, fitting the model via EM algorithm suffers from significant processing time. The main cause is due to the calculation of many multivariate t-cdfs (cumulative distribution functions) in E-step. In this article, we provide an approximate, but fast calculation method for the in univariate fashion, which is the product of successively conditional univariate t-cdfs with Taylor's first order approximation. By replacing all multivariate t-cdfs in E-step with the proposed approximate versions, we obtain the admissible results of fitting the model, where it gives 85% reduction time for the 5 dimensional skewness case of the Australian Institution Sport data set. For this approach, discussions about rough properties, advantages and limits are also presented.

• Smart Structures and Systems
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• 제14권3호
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• pp.377-395
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• 2014

Vibration-based fault detection and condition monitoring of rotating machinery, using statistical process control (SPC) combined with statistical pattern recognition methodology, has been widely investigated by many researchers. In particular, the discrete wavelet transform (DWT) is considered as a powerful tool for feature extraction in detecting fault on rotating machinery. Although DWT significantly reduces the dimensionality of the data, the number of retained wavelet features can still be significantly large. Then, the use of standard multivariate SPC techniques is not advised, because the sample covariance matrix is likely to be singular, so that the common multivariate statistics cannot be calculated. Even though many feature-based SPC methods have been introduced to tackle this deficiency, most methods require a parametric distributional assumption that restricts their feasibility to specific problems of process control, and thus limit their application. This study proposes a nonparametric multivariate control chart method, based on multiscale wavelet scalogram (MWS) features, that overcomes the limitation posed by the parametric assumption in existing SPC methods. The presented approach takes advantage of multi-resolution analysis using DWT, and obtains MWS features with significantly low dimensionality. We calculate Hotelling's $T^2$-type monitoring statistic using MWS, which has enough damage-discrimination ability. A bootstrap approach is used to determine the upper control limit of the monitoring statistic, without any distributional assumption. Numerical simulations demonstrate the performance of the proposed control charting method, under various damage-level scenarios for a bearing system.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.825-835
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• 2008

계량경제학 분야에서 널리 쓰이는 MGARCH(multivariate GARCH)모형은 여러개의 시계열자료들의 변동성을 함께 모형화한다. 그러나 변수가 많아질수록 추정해야 할 모수의 수가 급격하게 늘어나는 문제점이 있다. 본 연구에서는 인자 모형을 통해 자료의 차원을 축소시킴로써 이러한 문제를 해결하고자 하였다. 국내의 주가수익률 자료에 통계적 인자 모형과 fundamental factor model을 적용하여 각각의 의미 있는 인자들을 얻은 후 이를 MGARCH모형에 적합시켰다. 또한 두 인자모형을 바탕으로 얻어진 최종 모형들의 MSE, MAD와 VaR(Value at Risk)를 계산하여 예측력을 비교하고자 한다.

• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.881-889
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• 2009

Support vector machines(SVMs) are known as flexible and efficient classifier of multivariate observations, producing a hyperplane or hyperdimensional curved surface in multidimensional feature space that best separates training samples by known groups. As various methodological extensions are made for SVM classifiers in recent years, it becomes more difficult to understand the constructed model intuitively. The aim of this paper is to visualize various SVM classifications tuned by several parameters in reduced dimensions, so that data analysts secure the tangible image of the products that the machine made.

• 대한인간공학회지
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• 제6권1호
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• pp.3-8
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• 1987

This paper develops a statistical mode which estimates mental and physical loads of light work from sinus arrhythmia (SA) scores. During experiments, various levels of mental and physical loads (respectively scored by information processing and finger tapping rates) were imposed on subjects and SA scores were measured from the subjects. Two methods were used in developing workload estimation model. One is an algebraic inverse function of a multivariate regression equation, where mental and physical loads are independent variables and SA scores are dependent variables. The other is a statistical multivariate inverse regression. Of the two methods, inverse function resulted in larger mean squqre error in predicting mental and physical loads. Hence, inverse regression model is recommended for precise workload estimation.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.107-115
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• 2012

본 논문에서는 Yoo와 Cook (2007)에 의하여 제시된 다변량 회귀의 조건부 평균에 대한 최소 불일치 함수 접근법을 통한 최적 차원축소 부분공간의 추정에서 차원의 수가 추정된 선형결합들과 설명력 등에 어떤 영향을 미치는 지를 시뮬레이션 자료를 통하여 알아보았다. 그 결과 추정에 사용된 차원수에 따른 여러 결과들을 차원결정을 위한 검정과 함께 활용하면 모형에 필요한 차원수를 탐색하는데 매우 효과적임을 알 수 있었다.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.969-976
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• 2008

Mixed linear models have been widely used in various correlated data including multivariate survival data. In this paper we extend hierarchical-likelihood(h-likelihood) approach for mixed linear models with right censored data to that for left censored data. We also allow a general random-effect structure and propose the estimation procedure. The proposed method is illustrated using a numerical data set and is also compared with marginal likelihood method.