• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.221-229
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• 2018

The first Zagreb eccentricity index $E_1(G)$ of a graph G is defined as the sum of squares of the eccentricities of the vertices. In this paper some bounds for the first Zagreb eccentricity index and first Zagreb degree eccentricity index are computed.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.315-324
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• 2002

For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.48-54
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• 1995

A direct method for fitting analysis-of-variance models to unbalanced data is presented. This method exploits sparsity and rank deficiency of the matrix and is based on Gram-Schmidt orthogonalization of a set of sparse columns of the model matrix. The computational algorithm of the sum of squares for testing estmable hyphotheses is given.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.1029-1047
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• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.417-427
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• 1997

In this paper the parameter change problem in the stationary time series is considered. We propose a cumulative sum (CUSUM) of squares-type test statistic for detection of parameter changes in the AR(1) process. The proposed test statistic is based on the CUSIM of the squared observations and is shown to converge to a standard Brownian bridge. Simulations are performed to evaluate the performance of the proposed statistic and a real example is provided to illustrate the procedure.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.125-134
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• 2006

This study confirms that the regression model of endpoint of interval outputs is not identical with that of the other endpoint of interval outputs in interval regression models proposed by Tanaka et al. (1987) and constructs interval regression models using the best regression model given by variable selection. Also, this paper suggests a method to minimize the sum of lengths of a symmetric difference among observed and predicted interval outputs in order to estimate interval regression coefficients in the proposed model. Some examples show that the interval regression model proposed in this study is more accuracy than that introduced by Inuiguchi et al. (2001).

• Vacuum Magazine
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• v.2 no.1
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• pp.31-34
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• 2015

This article introduces fundamentals of self-diagnosis and predictive (or preventive) maintenance technologies for dry vacuum pumps. The state variables of dry pumps are addressed, such as the pump and motor body temperatures, consumption currents of main and booster pumps, mechanical vibration, and exhaust pressure, etc. The adaptive parametric models of the state variables of the dry pump are exploited to provide dramatic reduction of data size and computation time for self-diagnosis. Two indicators, the Hotelling's $T^2$ and the sum of squares residuals (Q), are illustrated to be quite effective and successful in diagnosing dry pumps used in the semiconductor processes.

• Journal of Applied Reliability
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• v.1 no.2
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• pp.165-173
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• 2001

The desirability function approach by Derringer and Suich (1980) and the generalized distance approach by Khuri and Conlon (1981) are two major approaches to multiresponse optimization for improvement of quality of a product or process. So far, the desirability function method has been the only tool for multiresponse optimization in the situations where there are the goal regions for the respective responses. For such situations, we propose a multiresponse optimization method based on the generalized distance approach.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.25
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• pp.103-113
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• 1992

This paper is to study the various diagnostic measures for detecting outliers and influential cases in linear regression. In this paper we review the most common diagnostic measures and show the inter-relationships the exist among them. Based on the PRESS(Predicted REsidual Sum of Squares ) offered by Allen(1974) as a criterion for model selection, we propose three measures for detecting outliers and influential cases. Examples are given illustrating various diagnostic measures including Proposed measures.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.549-553
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• 2011

In this paper, we deal with the problem of deciding the length of data for estimating the parameters in geometric Brownian motion. As an approach to this problem, we consider the change point test and introduce simple test statistic based on the cumulative sum of squares test (cusum test). A real data analysis is performed for illustration.