• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.369-388
• /
• 2023

In this paper, we develop the two-step procedure that detects and estimates the position of structural changes for multivariate nonstationary time series, either on mean parameters or second-order structures. We first investigate the presence of mean structural change by monitoring data through the aggregated cumulative sum (CUSUM) type statistic, a sequential procedure identifying the likely position of the change point on its trend. If no mean change point is detected, the proposed method proceeds to scan the second-order structural change by modeling the multivariate nonstationary time series with a multivariate locally stationary Wavelet process, allowing the time-localized auto-correlation and cross-dependence. Under this framework, the estimated dynamic spectral matrices derived from the local wavelet periodogram capture the time-evolving scale-specific auto- and cross-dependence features of data. We then monitor the change point from the lower-dimensional approximated space of the spectral matrices over time by applying the dynamic principal component analysis. Different from existing methods requiring prior information on the type of changes between mean and covariance structures as an input for the implementation, the proposed algorithm provides the output indicating the type of change and the estimated location of its occurrence. The performance of the proposed method is demonstrated in simulations and the analysis of two real finance datasets.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.42 no.2
• /
• pp.18-27
• /
• 2019

The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

• Communications for Statistical Applications and Methods
• /
• v.25 no.1
• /
• pp.71-78
• /
• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Journal of the Korean Statistical Society
• /
• v.25 no.1
• /
• pp.49-66
• /
• 1996

The singular value decomposition is one of the most useful methods in the area of matrix computation. It gives dimension reduction which is the centeral idea in many multivariate analyses. But this method is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, we derive the resistant version of singular value decomposition for principal component analysis. And we give its statistical applications to biplot which is similar to principal component analysis in aspects of the dimension reduction of an n x p data matrix. Therefore, we derive the resistant principal component analysis and biplot based on the resistant singular value decomposition. They provide graphical multivariate data analyses relatively little influenced by outlying observations.

• Communications for Statistical Applications and Methods
• /
• v.26 no.5
• /
• pp.519-526
• /
• 2019

Response dimension reduction in a sufficient dimension reduction (SDR) context has been widely ignored until Yoo and Cook (Computational Statistics and Data Analysis, 53, 334-343, 2008) founded theories for it and developed an estimation approach. Recent research in SDR shows that a semi-parametric approach can outperform conventional non-parametric SDR methods. Yoo (Statistics: A Journal of Theoretical and Applied Statistics, 52, 409-425, 2018) developed a semi-parametric approach for response reduction in Yoo and Cook (2008) context, and Yoo (Journal of the Korean Statistical Society, 2019) completes the semi-parametric approach by proposing an unstructured method. This paper theoretically discusses and provides insightful remarks on three versions of semi-parametric approaches that can be useful for statistical practitioners. It is also possible to avoid numerical instability by presenting the results for an orthogonal transformation of the response variables.

• Communications for Statistical Applications and Methods
• /
• v.7 no.2
• /
• pp.385-392
• /
• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.97-107
• /
• 2001

A simultaneous test criterion for multiple hypotheses concerning comparison of two multivariate normal populations is considered by using the so called Bayes factor method. Fully parametric frequentist approach for the test is not available and thus Bayesian criterion is pursued using a Bayes factor that eliminates its arbitrariness problem induced by improper priors. Specifically, the fractional Bayes factor (FBF) by O'Hagan (1995) is used to derive the criterion. Necessary theories involved in the derivation an computation of the criterion are provided. Finally, an illustrative simulation study is given to show the properties of the criterion.

• Communications for Statistical Applications and Methods
• /
• v.26 no.1
• /
• pp.35-46
• /
• 2019

Multivariate Confidence Region (MCR) cannot be used to obtain the confidence region of the mean vector of multivariate data when the normality assumption is not satisfied; however, the Quantile Confidence Region (QCR) could be used with a Multivariate Quantile Vector in these cases. The coverage rate of the QCR is better than MCR; however, it has a disadvantage because the QCR has a wide shape when the probability density function follows a bimodal form. In this study, we propose a Quantile Confidence Region using the Highest density (QCRHD) method with the Highest Density Region (HDR). The coverage rate of QCRHD was superior to MCR, but is found to be similar to QCR. The QCRHD is constructed as one region similar to QCR when the distance of the mean vector is close. When the distance of the mean vector is far, the QCR has one wide region, but the QCRHD has two smaller regions. Based on these features, it is found that the QCRHD can overcome the disadvantages of the QCR, which may have a wide shape.

• Journal of Ginseng Research
• /
• v.43 no.4
• /
• pp.508-516
• /
• 2019

Background: Ginsenosides are not only the principal bioactive components but also the important indexes to the quality assessment of Panax ginseng Meyer. Their contents in cultivated ginseng vary with the growth environment and age. The present study aimed at evaluating the significant difference between 36 cultivated ginseng of different cultivation areas and ages based on the simultaneously determined contents of 14 ginsenosides. Methods: A high-performance liquid chromatography (HPLC) coupled with triple quadrupole mass spectrometer (MS) method was developed and used in the multiple reaction-monitoring (MRM) mode (HPLC-MRM/MS) for the quantitative analysis of ginsenosides. Multivariate statistical analysis, such as principal component analysis and partial least squares-discriminant analysis, was applied to discriminate ginseng samples of various cultivation areas and ages and to discover the differentially accumulated ginsenoside markers. Results: The developed HPLC-MRM/MS method was validated to be precise, accurate, stable, sensitive, and repeatable for the simultaneous determination of 14 ginsenosides. It was found that the 3- and 5-yr-old ginseng samples were differentiated distinctly by all means of multivariate statistical analysis, whereas the 4-yr-old samples exhibited similarity to either 3- or 5-yr-old samples in the contents of ginsenosides. Among the 14 detected ginsenosides, Rg1, Rb1, Rb2, Rc, 20(S)-Rf, 20(S)-Rh1, and Rb3 were identified as potential markers for the differentiation of cultivation ages. In addition, the 5-yr-old samples were able to be classified in cultivation area based on the contents of ginsenosides, whereas the 3- and 4-yr-old samples showed little differences in cultivation area. Conclusion: This study demonstrated that the HPLC-MRM/MS method combined with multivariate statistical analysis provides deep insight into the accumulation characteristics of ginsenosides and could be used to differentiate ginseng that are cultivated in different areas and ages.

• Communications for Statistical Applications and Methods
• /
• v.24 no.1
• /
• pp.67-80
• /
• 2017

Over the last few decades, ensemble forecasts based on global climate models have become an important part of climate forecast due to the ability to reduce uncertainty in prediction. Moreover in ensemble forecast, assessing the prediction uncertainty is as important as estimating the optimal weights, and this is achieved through a probabilistic forecast which is based on the predictive distribution of future climate. The Bayesian model averaging has received much attention as a tool of probabilistic forecasting due to its simplicity and superior prediction. In this paper, we propose a new Bayesian model averaging method for probabilistic ensemble forecasting. The proposed method combines a deterministic ensemble forecast based on a multivariate regression approach with Bayesian model averaging. We demonstrate that the proposed method is better in prediction than the standard Bayesian model averaging approach by analyzing monthly average precipitations and temperatures for ten cities in Korea.