Multivariate response regression with low-rank and generalized sparsity

Cho Youngjin,Park Seyoung 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.3

In this study, we propose a multivariate-response regression by imposing structural conditions on the underlying regression coefficient matrix motivated by an analysis of Cancer Cell Line Encyclopedia (CCLE) data consisting of resistance responses to multiple drugs and gene expression of cancer cell lines. It is important to estimate the drug resistance response from gene information and identify those genes responsible for the sensitivity of the resistance response to each drug. We consider a penalized multiple-response regression estimator using both generalized ℓ₁ norm and nuclear norm regularizes based on the motivations that only a few genes are relevant to the effect of drug resistance responses and that some genes could have similar effects on multiple responses. For the statistical properties, we developed non-asymptotic error bounds of the proposed estimator. In our numerical analysis using simulated and CCLE data, the proposed method better predicts the drug responses than the other methods.

Multivariate Process Capability Index Using Inverted Normal Loss Function

Hye-Jin Moon(문혜진),Young-Bae Chung(정영배) 한국산업경영시스템학회 2018 한국산업경영시스템학회지 Vol.41 No.2

In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as Cp, Cpk,Cpm and have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index (????MC ) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

역정규 손실함수를 이용한 다변량 공정능력지수

문혜진,정영배 한국산업경영시스템학회 2018 한국산업경영시스템학회지 Vol.41 No.2

In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as Cp, Cpk, Cpm and C+pm have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index (MCpI) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

Comparison Analysis of Multivariate Process Capability Indices

Hye-Jin Moon,Young-Bae Chung 한국산업경영시스템학회 2019 한국산업경영시스템학회지 Vol.42 No.1

Recently, the manufacturing process system in the industrial field has become more and more complex and has been influenced by many and various factors. Moreover, these factors have the dependent correlation rather than independent of each other. Therefore, the statistical analysis has been extended from the univariate method to the multivariate method. The process capability indices have been widely used as statistical tools to assess the manufacturing process performance. Especially, the multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. The various multivariate process capability indices have been studying by many researchers in recent years. Hence, the purpose of the study is to compare the useful and various multivariate process capability indices through the simulation. Among them, we compare the useful models of several multivariate process capability indices such as MCpm, MC+pm and MCpl. These multivariate process capability indices are incorporates both the process variation and the process deviation from target or consider the expected loss caused by the process deviation from target. Through the computational examples, we compare these process capability indices and discuss their usefulness and effectiveness.

Bayesian latent factor regression for multivariate functional data with variable selection

노희상,최태련,박진수,정연승 한국통계학회 2020 Journal of the Korean Statistical Society Vol.49 No.3

In biomedical research, multivariate functional data are frequently encountered. Majority of the existing approaches for functional data analysis focus on univariate functional data and the methodology for multivariate functional data is far less studied. Particularly, the problem of investigating covariate effects on multivariate functional data has received little attention. In this research, we propose a fully Bayesian latent factor regression for studying covariate effects on multivariate functional data. The proposed model obtains a low-dimensional representation of multivariate functional data through basis expansions for splines and factor analysis for the basis coefficients. Then, the latent factors specific to each functional outcome are regressed onto covariates accounting for residual correlations among multiple outcomes. The assessment of covariate effects is conducted based on the marginal inclusion probability for each covariate, which is calculated a posteriori by assigning a stochastic search variable selection (SSVS) prior to the regression coefficients. To better control for the false discovery rate, we propose a multivariate SSVS prior that allows for a set of coefficients to be zero simultaneously. We illustrate the proposed method through a simulation study and an application to the air pollution data collected for 13 cities in China.

다변량 공정능력지수들의 비교분석

문혜진,정영배 한국산업경영시스템학회 2019 한국산업경영시스템학회지 Vol.42 No.1

Recently, the manufacturing process system in the industrial field has become more and more complex and has been influenced by many and various factors. Moreover, these factors have the dependent correlation rather than independent of each other. Therefore, the statistical analysis has been extended from the univariate method to the multivariate method. The process capability indices have been widely used as statistical tools to assess the manufacturing process performance. Especially, the multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. The various multivariate process capability indices have been studying by many researchers in recent years. Hence, the purpose of the study is to compare the useful and various multivariate process capability indices through the simulation. Among them, we compare the useful models of several multivariate process capability indices such as , and . These multivariate process capability indices are incorporates both the process variation and the process deviation from target or consider the expected loss caused by the process deviation from target. Through the computational examples, we compare these process capability indices and discuss their usefulness and effectiveness.

Bivariate regional frequency analysis of extreme rainfalls in Korea

Shin Ju-Young,Jeong Changsam,Ahn Hyunjun,Heo Jun-Haeng 한국수자원학회 2018 한국수자원학회논문집 Vol.51 No.9

다변량 빈도해석과 지역빈도해석의 장점을 동시에 가지는 다변량 지역빈도해석은 다양한 변수를 고려함으로써 수문 현상에 대하여 많은 정보를 얻을 수 있고 많은 가용 자료 수로 인하여 높은 정확도의 분석결과를 도출할 수 있다. 현재까지는 우리나라의 강우 자료를 이용하여 다변량 지역빈도해석이 시도된 적이 없어 국내의 강우 자료를 대상으로 다변량 지역빈도해석의 적용성을 검토할 필요가 있다. 본 연구에서는 다변량 지역빈도해석의 매개변수 추정, 최적 분포형 선정, 확률수문량 성장곡선 추정 등에 집중하여 이변량 수문자료인 연 최대 강우량-지속기간 자료에 대하여 이변 량 지역빈도해석의 적용성을 평가하였다. 기상청 71개 지점에 대하여 분석을 실시하였다. 본 연구를 통해 적용된 지역강우자료의 최적 copula 모형으로는 Frank와 Gumbel copula 모형이 선택되었고 주변분포형에 대해서는 지역별로 Gumbel과 대수정규분포와 같은 다양한 분포형이 최적 분포형으로 선택되었다. 상대제곱근오차(relative root mean square error)를 기준으로 지역빈도해석이 지점빈도해석보다 안정적이고 정확한 확률수문량 곡선 추정을 하였다. 이변량 강우분석에서 지역빈도해석을 적용하면 안정적인 수공구조물 설계기준 제시와 강우-지속기간 관계를 모형화 할 수 있을 것으로 기대된다. Multivariate regional frequency analysis has advantages of regional and multivariate framework as adopting a large number of regional dataset and modeling phenomena that cannot be considered in the univariate frequency analysis. To the best of our knowledge, the multivariate regional frequency analysis has not been employed for hydrological variables in South Korea. Applicability of the multivariate regional frequency analysis should be investigated for the hydrological variable in South Korea in order to improve our capacity to model the hydrological variables. The current study focused on estimating parameters of regional copula and regional marginal models, selecting the most appropriate distribution models, and estimating regional multivariate growth curve in the multivariate regional frequency analysis. Annual maximum rainfall and duration data observed at 71 stations were used for the analysis. The results of the current study indicate that Frank and Gumbel copula models were selected as the most appropriate regional copula models for the employed regions. Several distributions, e.g. Gumbel and log-normal, were the representative regional marginal models. Based on relative root mean square error of the quantile growth curves, the multivariate regional frequency analysis provided more stable and accurate quantiles than the multivariate at-site frequency analysis, especially for long return periods. Application of regional frequency analysis in bivariate rainfall-duration analysis can provide more stable quantile estimation for hydraulic infrastructure design criteria and accurate modelling of rainfall-duration relationship.

시변 조건부 상관관계모형의 비교: 다변량 GARCH 모형의 단순접근법

최완수 ( Wan Su Choi ) 한국창업정보학회 2006 창업정보학회지 Vol.9 No.3

The multivariate GARCH models are generally used in capturing the time-varying conditional correlations of financial data. While these models were used very frequently in finance because of simplicity, empirical applications would require further restrictions and more specific structures. Also it of ten difficult to verify the condition that the conditional covariance matrix of an estimated multivariate GARCH model is positive definite. Furthermore, such conditions are often very difficult to impose during the optimization of the log-likelihood function. This study suggests a simplified approach of multivariate GARCH model as an alternative model to extract the time-varying conditional correlation coefficients. This approach is very simple in that it only requires to estimate a univariate GARCH model of each return series. Therefore, this approach have the advantage that the estimation was very simple, and could avoid the problems of existing multivariate GARCH models. To verify this, diagonal vech(DVech) model, constant correlation(CC) model, BEKK model, and dynamic conditional correlation(DCC) model are used to compare with our approach. Using KOSPI200 stock index and its index futures returns, we firstly compare the correlation between the estimated conditional variances and covariances of each models. Also each elements of realized covariance matrix and the corresponding elements of estimated covariance matrix of each models are tested by linear regression model. Finally, the stationarity of optimal hedge ratio and hedged portfolio returns are compared by the standard deviation of them respectively. Empirical results show that our simplified approach could do relatively well compared with other existing multivariate GARCH models. In particular, the conditional correlation coefficient of our approach seems to almost completely track those of other models. These facts implied that our simplified approach of multivariate GARCH models can be an alternative model and used well in practice.

Multivariate Process Control Chart for Controlling the False Discovery Rate

Jang-Ho Park,Chi-Hyuck Jun 대한산업공학회 2012 Industrial Engineeering & Management Systems Vol.11 No.4

With the development of computer storage and the rapidly growing ability to process large amounts of data, the multivariate control charts have received an increasing attention. The existing univariate and multivariate control charts are a single hypothesis testing approach to process mean or variance by using a single statistic plot. This paper proposes a multiple hypothesis approach to developing a new multivariate control scheme. Plotted Hotelling’s T2 statistics are used for computing the corresponding p-values and the procedure for controlling the false discovery rate in multiple hypothesis testing is applied to the proposed control scheme. Some numerical simulations were carried out to compare the performance of the proposed control scheme with the ordinary multivariate Shewhart chart in terms of the average run length. The results show that the proposed control scheme outperforms the existing multivariate Shewhart chart for all mean shifts

Multivariate joint normal likelihood distance

Myung Geun Kim 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5

The likelihood distance for the joint distribution of two multivariate normal distributions with common covariance matrix is explicitly derived. It is useful for identifying outliers which do not follow the joint multivariate normal distribution with common covariance matrix. The likelihood distance derived here is a good ground for the use of a generalized Wilks statistic in influence analysis of two multivariate normal data. The likelihood distance for the joint distribution of two multivariate normal distributions with common covariance matrix is explicitly derived. It is useful for identifying outliers which do not follow the joint multivariate normal distribution with common covariance matrix. The likelihood distance derived here is a good ground for the use of a generalized Wilks statistic in influence analysis of two multivariate normal data.