• 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 the Korean Statistical Society
• /
• v.7 no.2
• /
• pp.109-119
• /
• 1978

When a response surface by a seconde order polynomial regression model, the stationary point is obtained by solving simultaneous linear equations. But the point is a function of random variables. We can find a confidence region for this point as Box and Hunter provided. However, the confidence region is often too large to be useful for the experiments, and it is necessary to augment additional design points in order to obtain a satisfactory confidence region for the stationary point. In this note, the author suggests a method how to augment design points "eficiently", and shows the change of the confidence region of the estimated stationary point in a response surface.e surface.

• Communications for Statistical Applications and Methods
• /
• v.24 no.6
• /
• pp.641-649
• /
• 2017

Multivariate confidence regions were defined using a chi-square distribution function under a normal assumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be obtained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.1
• /
• pp.179-187
• /
• 2013

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervals for fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.

• Structural Engineering and Mechanics
• /
• v.13 no.2
• /
• pp.117-134
• /
• 2002

This paper presents a computational method for a confidence region of identified parameters which are affected by measurement noise and error contained in prescribed parameters. The method is based on sensitivities of the identified parameters with respect to model parameter error and measurement noise along with the law of error propagation. By conducting numerical experiments on simple models, it is confirmed that the confidence region coincides well with the results of numerical experiments. Furthermore, the optimum arrangement of sensor locations is evaluated when uncertainty exists in prescribed parameters, based on the concept that square sum of coefficients of variations of identified results attains minimum. Good agreement of the theoretical results with those of numerical simulation confirmed validity of the theory.

• Communications for Statistical Applications and Methods
• /
• v.8 no.3
• /
• pp.581-588
• /
• 2001

The $ED_{100p}$ is that value of the dose associated with 100p% response rate in the analysis of quantal response data. Brand, Pinnock, and Jackson (1973) studied the confidence bands of $ED_{100p}$ obtained by solving extremal values algebraically on the ellipsoid confidence region of the parameters in the simple logistic regression model. In this paper, we develope and illustrate a simpler method for obtaining confidence bands for $ED_{100p}$ based on the rectangular confidence region of parameters.

• Communications for Statistical Applications and Methods
• /
• v.18 no.1
• /
• pp.103-110
• /
• 2011

Exponential distribution is widely adopted as a lifetime model. Many authors have considered the interval estimation of the parameters of two-parameter exponential distribution based on complete and censored samples. In this paper, we consider the interval estimation of the location and scale parameters and the joint confidence region of the parameters of two-parameter exponential distribution based on upper records. A simulation study is done for the performance of all proposed confidence intervals and regions. We also propose the predictive intervals of the future records. Finally, a numerical example is given to illustrate the proposed methods.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.1
• /
• pp.1226-1230
• /
• 2001

Multi-target tracking systems need to tracking several targets simultaneously. To track a target among the measurements of several targets, data association is needed. In this paper, a method using the cou-pled confidence region of predicted target position is proposed. The proposed method shows good performance in simulations of multi-target tracking systems.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.53 no.5
• /
• pp.132-140
• /
• 2016

In this paper, we propose boundary-preserving stereo matching method based on adaptive disparity adjustment using confidence region detection. To find the initial disparity map, we compute data cost using the color space (CIE Lab) combined with the gradient space and apply double cost aggregation. We perform left/right consistency checking to sort out the mismatched region. This consistency check typically fails for occluded and mismatched pixels. We mark a pixel in the left disparity map as "inconsistent", if the disparity value of its counterpart pixel differs by a value larger than one pixel. In order to distinguish errors caused by the disparity discontinuity, we first detect the confidence map using the Mean-shift segmentation in the initial disparity map. Using this confidence map, we then adjust the disparity map to reduce the errors in initial disparity map. Experimental results demonstrate that the proposed method produces higher quality disparity maps by successfully preserving disparity discontinuities compared to existing methods.

• Journal of Korean Society for Quality Management
• /
• v.30 no.4
• /
• pp.44-57
• /
• 2002

In this paper we study two vector-valued process capability indices $C_{p}$＝($C_{px}$, $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) considering process capability indices $C_{p}$ and $C_{pk}$. First, we derive two asymptotic distributions of plug-in estimators (equation omitted) and (equation omitted) under. some proper. conditions. Second, we examine the performance of asymptotic confidence regions of our process capability indices $C_{p}$＝( $C_{px}$ , $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) under BN($\mu$$_{x}$, $\mu$$_{y}$, $\sigma$$^2$$_{x}$, $\sigma$$^2$$_{y}$,$\rho$)$\rho$)EX>)EX>)EX>)