• Communications for Statistical Applications and Methods
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• 제27권3호
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• pp.377-383
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• 2020

The likelihood-based inference in a nonlinear generalized mixed model often requires computing moments of truncated multivariate normal random variables. Many methods have been proposed for the computation using a recurrence relation or the moment generating function; however, these methods rely on high dimensional numerical integrations. The numerical method is known to be inefficient for high dimensional integral in accuracy. Besides the accuracy, the methods demand too much computing time to use them in practical analyses. In this note, a moment calculation method is proposed under an assumption of a certain covariance structure that occurred mostly in generalized mixed models. The method needs only low dimensional numerical integrations.

• 응용통계연구
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• 제17권1호
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• pp.165-172
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• 2004

최근 다변량자료 분석과 관련하여 이를 시스템으로 구현하려는 연구가 다양한 각도로 이루어지고 있다. 이러한 연구들의 공통적인 특징은 일반 사용자들에게 고급 통계분석기법을 편리하게 활용할 수 있도록 GUI(Graphical User Interface) 환경의 시스템을 제공해 준 것이다. 이러한 연구들의 연장선상에서, 본 연구에서는 사회 각 분야에서 가장 널리 활용되고 있는 사무용 프로그램 인 Excel을 활용하여 시스템을 개발함으로써, 일반 사용자들도 대화식으로 다변량자료 분석을 쉽게 수행할 수 있도록 하였다.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.673-679
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• 2021

The moment calculation in a truncated multivariate normal distribution is a long-standing problem in statistical computation. Recently, Kan and Robotti (2017) developed an algorithm able to calculate all orders of moment under different types of truncation. This result was implemented in an R package MomTrunc by Galarza et al. (2021); however, it is difficult to use the package in practical statistical problems because the computational burden increases exponentially as the order of the moment or the dimension of the random vector increases. Meanwhile, Lee (2021) presented an efficient numerical method in both accuracy and computational burden using Gauss-Hermit quadrature. This article introduces trunmnt implementation of Lee's work as an R package. The Package is believed to be useful for moment calculations in most practical statistical problems.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.39-46
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• 2005

We propose an equivariant and robust estimator in multivariate regression model based on the least quartile difference (LQD) estimator in univariate regression. We call this estimator as the multivariate least quartile difference (MLQD) estimator. The MLQD estimator considers correlations among response variables and it can be shown that the proposed estimator has the appropriate equivariance properties defined in multivariate regressions. The MLQD estimator has high breakdown point as does the univariate LQD estimator. We develop an algorithm for MLQD estimate. Simulations are performed to compare the efficiencies of MLQD estimate with coordinatewise LQD estimate and the multivariate least trimmed squares estimate.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.1037-1046
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• 2003

We propose an equivariant and robust estimator in multivariate regression model based on the least trimmed squares (LTS) estimator in univariate regression. We call this estimator as multivariate least trimmed squares (MLTS) estimator. The MLTS estimator considers correlations among response variables and it can be shown that the proposed estimator has the appropriate equivariance properties defined in multivariate regression. The MLTS estimator has high breakdown point as does LTS estimator in univariate case. We develop an algorithm for MLTS estimate. Simulation are performed to compare the efficiencies of MLTS estimate with coordinatewise LTS estimate and a numerical example is given to illustrate the effectiveness of MLTS estimate in multivariate regression.

• 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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• 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.

• Communications for Statistical Applications and Methods
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• 제30권4호
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• pp.389-402
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• 2023

Multivariate or clustered failure time data often occur in many medical, epidemiological, and socio-economic studies when survival data are collected from several research centers. If the data are periodically observed as in a longitudinal study, survival times are often subject to various types of interval-censoring, creating multivariate interval-censored data. Then, the event times of interest may be correlated among individuals who come from the same cluster. In this article, we propose a unified linear regression method for analyzing multivariate interval-censored data. We consider a semiparametric multivariate accelerated failure time model as a statistical analysis tool and develop a generalized Buckley-James method to make inferences by imputing interval-censored observations with their conditional mean values. Since the study population consists of several heterogeneous clusters, where the subjects in the same cluster may be related, we propose a generalized estimating equations approach to accommodate potential dependence in clusters. Our simulation results confirm that the proposed estimator is robust to misspecification of working covariance matrix and statistical efficiency can increase when the working covariance structure is close to the truth. The proposed method is applied to the dataset from a diabetic retinopathy study.

• Communications for Statistical Applications and Methods
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• 제20권2호
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• pp.129-136
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• 2013

Linear regression is the most basic statistical model for exploring the relationship between a numerical response variable and several explanatory variables. Logistic regression secures the role of linear regression for the dichotomous response variable. In this paper, we propose a biplot-type display of the multivariate data guided by the linear regression and/or the logistic regression. The figures show the directional flow of the response variable as well as the interrelationship of explanatory variables.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.237-247
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• 2001

In this paper, we will introduce multivariate versions of bivariate conditionally positive dependence and the partial ordering is developed among conditionally positive lower orthant dependent(CPLOD) random vectors. This permits us to measure the degree of CPLOD-ness and to compare pairs of CPLOD random vectors. Some proper ties and closure under certain statistical operations are derived.