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

• Communications for Statistical Applications and Methods
• /
• v.10 no.3
• /
• pp.1037-1046
• /
• 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
• /
• v.28 no.5
• /
• pp.553-562
• /
• 2021

Directional regression (DR; Li and Wang, 2007) is well-known as an exhaustive sufficient dimension reduction method, and performs well in complex regression models to have linear and nonlinear trends. However, the extension of DR is not well-done upto date, so we will extend DR to accommodate multivariate regression and large p-small n regression. We propose three versions of DR for multivariate regression and discuss how DR is applicable for the latter regression case. Numerical studies confirm that DR is robust to the number of clusters and the choice of hierarchical-clustering or pooled DR.

• Communications for Statistical Applications and Methods
• /
• v.12 no.1
• /
• pp.39-46
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.679-688
• /
• 2008

In multivariate regression analysis there exist many influence measures on the regression estimates. However it seems to be few of influence diagnostics on test statistics in hypothesis testing. Case-deletion approach is fundamental for investigating influence of observations on estimates or statistics. Tang and Fung (1997) derived single case-deletion of the Wilks' ratio, Lawley-Hotelling trace, Pillai's trace for testing a general linear hypothesis of the regression coefficients in multivariate regression. In this paper we derived more extended form of those measures to deal with joint influence among observations. A numerical example is given to illustrate the effect of joint influence on the test statistics.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.473-478
• /
• 2002

A test for a single outlier in multivariate regression with linear constraints on regression coefficients using a mean shift model is derived. It is shown that influential observations based on case-deletions in testing linear hypotheses are determined by two types of outliers that are mean shift outliers with or without linear constraints, An illustrative example is given.

• Journal of the Korean Statistical Society
• /
• v.11 no.1
• /
• pp.59-68
• /
• 1982

We propose that, in order to control the inflation and general instability associated with the least squares estimates, we can use the ridge estimator $$ \hat{B}^* = (X'X+kI)^{-1}X'Y : k \leq 0$$ for the regression coefficients B in multivariate regression. Our hope is that by accepting some bias, we can achieve a larger reduction in variance. We show that such a k always exists and we derive the formula obtaining k in multivariate ridge regression.

• Communications for Statistical Applications and Methods
• /
• v.20 no.2
• /
• pp.129-136
• /
• 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.

• Proceedings of the KSME Conference
• /
• 2007.05a
• /
• pp.250-255
• /
• 2007

Steam generator tubes play an important role in safety because they constitute one of the primary barriers between the radioactive and non-radioactive sides of the nuclear power plant. For this reason, the integrity of the tubes is essential in minimizing the leakage possibility of radioactive water. The integrity of the tubes is evaluated based on NDE (non-destructive evaluation) inspection results. Especially ECT (eddy current test) method is usually used for detecting the flaws in steam generator tubes. However, detection capacity of the NDE is not perfect and all of the "real flaws" which actually existing in steam generator tunes is not known by NDE results. Therefore reliability of NDE system is one of the essential parts in assessing the integrity of steam generators. In this study POD (probability of detection) of ECT system for ODSCC in steam generator tubes is evaluated using multivariate logistic regression. The cracked tube specimens are made using the withdrawn steam generator tubes. Therefore the cracks are not artificial but real. Using the multivariate logistic regression method, continuous POD surfaces are evaluated from hit (detection) and miss (no detection) binary data obtained from destructive and non-destructive evaluation of the cracked tubes. Length and depth of cracks are considered in multivariate logistic regression and their effects on detection capacity are evaluated.

• Proceedings of the Korean Statistical Society Conference
• /
• 2000.11a
• /
• pp.187-191
• /
• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.