• Communications for Statistical Applications and Methods
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• v.25 no.1
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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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• v.30 no.5
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• pp.453-465
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• 2023

The prediction problem of univariate records, though not addressed in multivariate records, has been discussed by many authors based on records values. There are various definitions for multivariate records among which depth-based records have been selected for the aim of this paper. In this paper, by means of the maximum likelihood and conditional median methods, point and interval predictions of depth values which are related to the future depth-based multivariate records are considered on the basis of the observed ones. The observations derived from some elements of the elliptical distributions are the main reason of studying this problem. Finally, the satisfactory performance of the prediction methods is illustrated via some simulation studies and a real dataset about Kermanshah city drought.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1047-1057
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• 2009

The nonparametric bivariate two-sample test of Bennett (1967) is extended to the multivariate k sample test. This test has been easily modified for a monotone trend among k samples. Often in applications it is important to consider a set of multivariate response variables simultaneously, rather than individually, and also important to consider testing k samples altogether. Different approaches of estimating the null covariance matrices of the test statistics resulted in the same limiting form. The multivariate k sample test is applied to the non-normal data of a randomized trial conducted for a period of four weeks in mental hospitals. The purpose of the trial is to compare the efficacy of three different interventions for a relief of the frequently occurring problems of constipation, caused as a side effect of antipsychotic drugs during hospitalization. The bowel movement status of patient for a week is summarized into a single severity score, and severity scores of four weeks comprise a four-dimensional multivariate variable. It is desirable with this trial data to consider a multivariate testing among k samples.

• Journal of Korean Society for Quality Management
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• v.49 no.4
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• pp.539-550
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• 2021

Purpose: The purpose of this study is to propose a multivariate CUSUM control chart that can detect the out-of-control state fast while monitoring the cross- and auto- correlated multivariate time series data. Methods: We first build models to estimate the observation data and calculate the corresponding residuals. After then, a multivariate CUSUM chart is applied to monitor the residuals instead of the original raw observation data. Vector Autoregression and Artificial Neural Net are selected for the modelling, and Separated-MCUSUM chart is selected for the monitoring. The suggested methods are tested under a number of experimental settings and the performances are compared with those of other existing methods. Results: We find that Artificial Neural Net is more appropriate than Vector Autoregression for the modelling and show the combination of Separated-MCUSUM with Artificial Neural Net outperforms the other alternatives considered in this paper. Conclusion: The suggested chart has many advantages. It can monitor the complicated multivariate data with cross- and auto- correlation, and detects the out-of-control state fast. Unlike other CUSUM charts finding their control limits by trial and error simulation, the suggested chart saves lots of time and effort by approximating its control limit mathematically. We expect that the suggested chart performs not only effectively but also efficiently for monitoring the process with complicated correlations and frequently-changed parameters.

• Journal of the Korean Statistical Society
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• v.15 no.2
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• pp.107-117
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• 1986

This paper gives some new results on the multivariate linear calibration problem in the case when the controlled variable is univariate. Firstly, a condition under which one can obtain a finite closed confidence interval of $x_0$(unknown controlled variable) is suggested. Secondly, this article considers a criterion to find out whether the multivariate calibration significantly shortens the confidence interval of $x_0$ and supports this criterion by examples. Finally, a multivariate extension of the results in Lwin Maritz (1982) is given.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.177-186
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• 2003

The Zero-Inflated Poisson regression is a model for count data with exess zeros. When the correlated response variables are intrested, we have to extend the univariate zero-inflated regression model to multivariate model. In this paper, we study and simulate the multivariate zero-inflated regression model. A real example was applied to this model. Regression parameters are estimated by using MLE's. We also compare the fitness of multivariate zero-inflated Poisson regression model with the decision tree model.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. 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 two non-normal distributions.

• Journal of the Korean Magnetic Resonance Society
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• v.22 no.3
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• pp.46-53
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• 2018

NMR-based metabolomics needs various knowledge to elucidate metabolic perturbation such as NMR experiments, NMR spectrum processing, raw data processing, metabolite identification, statistical analysis, and metabolic pathway analysis regarding technical aspects. Among them, some concepts of raw data processing and multivariate analysis are not easy to understand but are important to correctly interpret metabolic profile. This article introduces NMR spectrum processing, raw data processing, and multivariate analysis.

• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.55-69
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• 2006

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1013-1021
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• 2003

Huffer and Park (2002) proposed a chi-squared test for multivariate structure. Their test detects the deviation of data from mutual independence or multivariate normality. We will compute the Rao-Robson chi-squared version of the test, which is easy to apply in practice since it has a limiting chi-squared distribution. We will provide a self-contained argument that it has a limiting chi-squared distribution. We study the accuracy in finite samples of the limiting distribution. We finally compare the power of our test with those of other popular normality tests in an application to a real data.