• 호남수학학술지
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• 제45권3호
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• pp.503-512
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• 2023

In the present article, we introduce the concepts of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence for sequences in g-metric spaces. We investigate some properties and relationships among these new concepts.

• 대한수학회보
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• 제35권4호
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• pp.741-755
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• 1998

We prove the asymptotic lens equivalence in manifolds without conjugate points. By using this property we show that under a metric condition of asymptotically Euclidean and the curvature condition decaying faster than quadratic, any surface $(R^2,g)$ without conjugate points is Euclidean.

• 호남수학학술지
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• 제43권2호
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• pp.343-357
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• 2021

In the present paper, we introduce the concepts of $\mathcal{I}$-asymptotically statistical $\tilde{\phi}$-equivalence and $\mathcal{I}$-asymptotically lacunary statistical $\tilde{\phi}$-equivalence for triple sequences. Moreover, we give the relations between these new notions.

• 호남수학학술지
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• 제43권1호
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2000년도 추계학술대회
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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).

• 대한수학회보
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• 제55권4호
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• pp.1303-1315
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• 2018

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method [11] to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in [24]. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.

• Communications for Statistical Applications and Methods
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• 제16권6호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제37권1호
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• pp.1-13
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• 1998

In this paper, we have represented the efficient way how to enumerate the optimal number-right scores to adjust the item difficulty and to improve item discrimination. To estimate the optimal number-right scores in two equivalent math-tests by linear score equating a measurement error model was applied to the true scores observed from a pair of equivalent math-tests assumed to measure same trait. The model specification for true scores which is represented by the bivariate model is a simple regression model to inference the optimal number-right scores and we assume again that the two simple regression lines of raw scores and true scores are independent each other in their error models. We enumerated the difference between mean value of $\chi$＊ and ${\mu}$$\_$$\chi$/ and the difference between the mean value of y＊and a＋b${\mu}$$\_$$\chi$/ by making an inference the estimates from 2 error variable regression model. Furthermore, so as to distinguish from the original score points, the estimated number-right scores y’$\^$*/ as the estimated regression values of true scores with the same coordinate were moved to center points that were composed of such difference values with result of such parallel score moving procedure as above mentioned. We got the asymptotically normal distribution in Figure 5 that was represented as the optimal distribution of the optimal number-right scores so that we could decide the optimal proportion of number-right score in each item. Also by assumption that equivalence of two tests is closely connected to unidimensionality of a student’s ability. we introduce new definition of trait score to evaluate such ability in each item. In this study there are much limitations in getting the real true scores and in analyzing data of the bivariate error model. However, even with these limitations we believe that this study indicates that the estimation of optimal number right scores by using this enumeration procedure could be easily achieved.

• 한국전산구조공학회논문집
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• 제24권2호
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• pp.149-156
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• 2011

본 논문에서는 생브낭의 원리를 이용하여 보/판/쉘 등의 구조물에서 응력분포를 후처리함으로써 개선할 수 있는 방법을 개발하였다. 생브낭의 원리에 따르면, 주어진 탄성문제에 대해서 실제의 응력분포에 상관없이 합응력들로 문제를 기술할 수 있다. 현재까지 알려진 바에 따르면 유일하게 점근적으로 타당한 이론들은 Euler-Bernoulli(E-B) 보이론과 Kirchhoff-Love(K-L) 판이론 등이 있다. 많은 공학적 문제들이 이 두 이론들에 기초하여 해석되어 왔음은 주지의 사실이다. 하지만, 현대의 공학 문제들은 보다 정확한 해석기법을 요구한다. 본 연구에서는 자유도가 상대적으로 많은 고차이론 등을 사용하지 않고, 고전적인 E-B 또는 K-L 해석결과를 합응력 등가의 원리를 이용하여 후처리함으로써 변위 및 응력분포를 정확하게 예측할 수 있는 방법을 개발하였고, 이방성 보 수치예제를 통해 제안된 방법론을 탄성해석법과 비교 검증하였다.