• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.93-103
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• 2005

We study some stability properties and asymptotic behavior for linear difference systems by using the results in [W. F. Trench: Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Comput. Math. Appl. 36 (1998), no. 10-12, pp. 261-267].

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.177-184
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• 2007

We study the asymptotic behavior of nonlinear Volterra difference system $$x(n+1)=f(n,x(n))+{\sum\limits^{n}_{s=n_{o}}\;g(n,s,x(s)),\;x(n_{o})=xo$$ by using the resolvent matrix R(n, m) of the corresponding linear Volterra system and the comparison principle.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.363-363
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• 2000

We derive an asymptotic relation between the scores for the censored and uncensored observations for the untied value case among uncensored observations. With this relation, we show that two types of the linear rank statistics which are based on any consistent estimates of the distribution function, are asymptotically equivalent. Also, we discuss another asymptotic equivalence considered by Cuzick (1985).

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.663-675
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• 2007

We investigate the representation of the solution of discrete linear Volterra difference systems by means of the resolvent matrix and fundamental matrix, respectively, and then study the boundedness of the solutions of discrete Volterra systems by improving the assumptions and the proofs of Medina#s results in [6].

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.3-11
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• 1981

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased (MVU) estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distirubtions are Weibull with unknown scale parameters and same known shape parameter. The asymptotic distribution of MVU estimate of system reliability in the model is obtained by using the standard asymptotic properties of the maximum likelihood estimate of system reliability and establishing their equivalence. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability. Empirical comparison of the two estimates for small samples is studies by Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.605-613
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• 2015

A three-arm parallel design has been proposed to assess the biosimilarity between a biological product and a reference product using relative distance (Kang and Chow, 2013). The three-arm parallel design consists of two arms for the reference product and one arm for the biosimilar product. This paper extended the three-arm parallel design to a (k + 1)-arm parallel design composed of k (${\geq}3$) arms for the reference product and one arm for the biosimilar product. A new relative distance was defined based on Euclidean distance; consequently, a corresponding test procedure was developed based on asymptotic distribution. Type I error rates and powers were investigated both theoretically and empirically.

• Communications for Statistical Applications and Methods
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• v.16 no.6
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• pp.989-995
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• 2009

Basu et al. (1998) proposed the minimum divergence estimating method which is free from using the painful kernel density estimator. Their proposed class of density power divergences is indexed by a single parameter $\alpha$ which controls the trade-off between robustness and efficiency. In this article, (1) we introduce a new large class the minimum squared distance which includes from the minimum Hellinger distance to the minimum $L_2$ distance. We also show that under certain conditions both the minimum density power divergence estimator(MDPDE) and the minimum squared distance estimator(MSDE) are asymptotically equivalent and (2) in finite samples the MDPDE performs better than the MSDE in general but there are some cases where the MSDE performs better than the MDPDE when estimating a location parameter or a proportion of mixed distributions.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.289-304
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• 2012

In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(g(t)))=0$$ and $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(h(t)))=0$$ on an arbitrary time scale $\mathbb{T}$ with sup $\mathbb{T}={\infty}$, where n is a positive integer, ${\delta}=1$ or -1 and $$S_k(t,x)=\{\array x(t),\;if\;k=0,\\a_k(t)S_{{\kappa}-1}^{\Delta}(t),\;if\;1{\leq}k{\leq}n-1,\\a_n(t)[S_{{\kappa}-1}^{\Delta}(t)]^{\alpha},\;if\;k=n,$$ with ${\alpha}$ being a quotient of two odd positive integers and every $a_k$ ($1{\leq}k{\leq}n$) being positive rd-continuous function. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.250-255
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• 2012

Face recognition has wide applications in security and surveillance systems as well as in robot vision and machine interfaces. Conventional challenges in face recognition include pose, illumination, and expression, and face recognition at a distance involves additional challenges because long-distance images are often degraded due to poor focusing and motion blurring. This study investigates the effectiveness of applying photon-counting linear discriminant analysis (Pc-LDA) to face recognition in harsh environments. A related technique, Fisher linear discriminant analysis, has been found to be optimal, but it often suffers from the singularity problem because the number of available training images is generally much smaller than the number of pixels. Pc-LDA, on the other hand, realizes the Fisher criterion in high-dimensional space without any dimensionality reduction. Therefore, it provides more invariant solutions to image recognition under distortion and degradation. Two decision rules are employed: one is based on Euclidean distance; the other, on normalized correlation. In the experiments, the asymptotic equivalence of the photon-counting method to the Fisher method is verified with simulated data. Degraded facial images are employed to demonstrate the robustness of the photon-counting classifier in harsh environments. Four types of blurring point spread functions are applied to the test images in order to simulate long-distance acquisition. The results are compared with those of conventional Eigen face and Fisher face methods. The results indicate that Pc-LDA is better than conventional facial recognition techniques.