• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.333-344
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• 2012

We consider some statistical properties of the first order difference-based error variance estimator in nonparametric regression models with a single outlier. So far under an outlier(s) such difference-based estimators has been rarely discussed. We propose the first order difference-based estimator using the leave-one-out method to detect a single outlier and simulate the outlier detection in a nonparametric regression model with the single outlier. Moreover, the outlier detection works well. The results are promising even in nonparametric regression models with many outliers using some difference based estimators.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.299-309
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• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.6
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• pp.331-337
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• 2018

This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Wind and Structures
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• v.32 no.3
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• pp.193-204
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• 2021

The estimation of the extreme wind load (effect) under a mean recurrence interval (MRI) is an important task in the wind-resistant design for the structure. It can be predicted by either first-order method or full-order method, depending on the accuracy and complexity requirement. Although the first-order method with the consideration of wind directionality has been proposed, less work has been done on the full-order method, especially with the wind directionality. In this study, the full-order method considering the wind directionality is proposed based on multivariate joint probability distribution. Meanwhile, considering two wind directions, the difference of the corresponding results based on the first-order method and full-order method is analyzed. Finally, based on the measured wind speed data, the discrepancy between these two methods is investigated. Results show that the difference between two approaches is not obvious under larger MRIs while the underestimation caused by the first-order method can be larger than 15% under smaller MRIs. Overall, the first-order method is sufficient to estimate the extreme wind load (effect).

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.135-144
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• 2005

In this paper, we develop the noninformative priors for the exponential models when the parameter of interest is the difference of two means. We develop the first and second order matching priors. We reveal that the second order matching priors do not exist. It turns out that Jeffreys' prior does not satisfy a first order matching criterion. The Bayesian credible intervals based on the first order matching meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.431-442
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• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1067-1078
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• 2005

In this paper, we develop the noninformative priors for the exponential models when the parameter of interest is the difference of two means. We develop the first and second order matching priors. We reveal that the second order matching priors do not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order matching meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.