• Journal of the Korean Data and Information Science Society
• /
• v.26 no.6
• /
• pp.1537-1545
• /
• 2015

Support vector quantile regression (SVQR) can be obtained by applying support vector machine with a check function instead of an e-insensitive loss function into the quantile regression, which still requires to solve a quadratic program (QP) problem which is time and memory expensive. In this paper we propose an SVQR whose objective function is composed of an asymmetric quadratic loss function. The proposed method overcomes the weak point of the SVQR with the check function. We use the iterative procedure to solve the objective problem. Furthermore, we introduce the generalized cross validation function to select the hyper-parameters which affect the performance of SVQR. Experimental results are then presented, which illustrate the performance of proposed SVQR.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.2
• /
• pp.449-455
• /
• 2004

Support vector machine (SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval regression models for crisp input-output data. The proposed method is based on quadratic loss SVM, which implements quadratic programming approach giving more diverse spread coefficients than a linear programming one. The proposed algorithm here is model-free method in the sense that we do not have to assume the underlying model function. Experimental result is then presented which indicate the performance of this algorithm.

• Communications for Statistical Applications and Methods
• /
• v.7 no.3
• /
• pp.767-772
• /
• 2000

Zellner(1994) introduced the notion of a balanced loss function in the context of a general liner model to reflect both goodness of fit and precision of estimation. We study the perspective of unifying a variety of results both frequentist and Bayesian from Poisson distributions. We show that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for Poisson distribution.

• Communications for Statistical Applications and Methods
• /
• v.17 no.2
• /
• pp.183-191
• /
• 2010

Support vector quantile regression(SVQR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. In this paper we propose an iterative reweighted least squares(IRWLS) procedure to solve the problem of SVQR with a weighted quadratic loss function. Furthermore, we introduce the generalized approximate cross validation function to select the hyperparameters which affect the performance of SVQR. Experimental results are then presented which illustrate the performance of the IRWLS procedure for SVQR.

• Journal of Korean Society for Quality Management
• /
• v.30 no.3
• /
• pp.66-78
• /
• 2002

Process capability indices are being used as indicators for measurements of process capability for SPC of quality assurance system in industries. In view of the enhancement of customer satisfaction, process capability indices in which loss functions are used to deal with the economic loss In the processes deviated from the target, are in an adequate representation of the customer's perception of quality In this connection, the loss function has become increasingly important in quality assurance. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider the proximity to the target while assessing its quality. But this traditional quadratic loss function is inadequate to assessing the quality and quality improvement since different processes have different sets of economic consequences on the manufacturing, Thereby, a flexible approach to the development of the loss function needs to be desired. In this paper, we introduce an easily understood loss function, based on reflection of probability density function of the normal distribution. That is, the Reflected Normal Loss function can be adapted to an asymmetric loss as well as to a symmetric loss around the target. We propose that, instead of the process variation, a new capability index, CpI using the Reflected Normal Loss Function that can accurately reflect the losses associated with the process and a new capability index CpI Is compared with the classical indices as $C_{p}$ , $C_{pk}$, $C_{pm}$ and $C_{pm}$ $^{+}$.>.+/./.

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.04a
• /
• pp.1-6
• /
• 2005

In this paper we propose how to simultaneously optimize multiple responses for robust design when data are collected from a combined array. The proposed method is based on the quadratic loss function. An example is illustrated to show the proposed method.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.2
• /
• pp.255-261
• /
• 2005

Many designed experiments require the simultaneous optimization of multiple responses. In this paper, we propose how to simultaneously optimize multiple responses for robust design when data are collected from a combined array. The proposed method is based on the quadratic loss function. An example is illustrated to show the proposed method.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.39 no.2
• /
• pp.37-45
• /
• 2016

Control chart is representative tools of statistical process control (SPC). It is a graph that plotting the characteristic values from the process. It has two steps (or Phase). First step is a procedure for finding a process parameters. It is called Phase I. This step is to find the process parameters by using data obtained from in-controlled process. It is a step that the standard value was not determined. Another step is monitoring process by already known process parameters from Phase I. It is called Phase II. These control chart is the process quality characteristic value for management, which is plotted dot whether the existence within the control limit or not. But, this is not given information about the economic loss that occurs when a product characteristic value does not match the target value. In order to meet the customer needs, company not only consider stability of the process variation but also produce the product that is meet the target value. Taguchi's quadratic loss function is include information about economic loss that occurred by the mismatch the target value. However, Taguchi's quadratic loss function is very simple quadratic curve. It is difficult to realistically reflect the increased amount of loss that due to a deviation from the target value. Also, it can be well explained by only on condition that the normal process. Spiring proposed an alternative loss function that called reflected normal loss function (RNLF). In this paper, we design a new control chart for overcome these disadvantage by using the Spiring's RNLF. And we demonstrate effectiveness of new control chart by comparing its average run length (ARL) with ${\bar{x}}-R$ control chart and expected loss control chart (ELCC).

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.36 no.2
• /
• pp.56-62
• /
• 2013

Control chart is representative tool of Statistical Process Control (SPC). But, it is not given information about the economic loss that occurs when a product is produced characteristic value does not match the target value of the process. In order to manage the process, we should consider not only stability of the variation also produce products with a high degree of matching the target value that is most ideal quality characteristics. There is a need for process control in consideration of economic loss. In this paper, we design a new control chart using the quadratic loss function of Taguchi. And we demonstrate effectiveness of new control chart by compare its ARL with ${\overline{x}}-R$ control chart.

• 한국데이터정보과학회:학술대회논문집
• /
• 2004.10a
• /
• pp.53-59
• /
• 2004

Support vector machine(SVM) approach to regression can be found in information science literature. SVM implements the regularization technique which has been introduced as a way of controlling the smoothness properties of regression function. In this paper, we propose a new estimation method based on quadratic loss SVM for a linear fuzzy regression model of Tanaka's, and furthermore propose a estimation method for nonlinear fuzzy regression. This approach is a very attractive approach to evaluate nonlinear fuzzy model with crisp input and output data.