• East Asian mathematical journal
• /
• 제5권1호
• /
• pp.95-110
• /
• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• 통상정보연구
• /
• 제9권2호
• /
• pp.65-86
• /
• 2007

This paper reviews the properties and application methods of widely used types of risk measures, identifies the rationale and business-side effects of hedging, derives the theoretical formula of optimal hedging ratio, and analyzes the various functional aspects of VaR(Value-at-risk) as a risk measure and a hedging tool. Especially this paper focuses on the characteristics of VaR compared with other risk measures in terms of their own principal determinants and identifies its stronger aspects in the dimension of hedging strategy tools. As well, this paper provides the detailed processes deriving the optimal hedge ratios based on the distributional parameters and risk factors. In addition, this paper presents the detailed and substantial processes of estimating the minimum variance hedge ratio and minimum-VaR hedge ratio using the actual data and shows that the minimum variance hedge ratio proves helpful for many cases although it is not appropriate for the non-linear portfolio including the option contracts. We demonstrate the trade-off relationship between the minimum variance hedge strategy and the minimum-VaR hedge strategy in their hedging costs and performances through calculation of the respective VaRs and variances of unhedged and hedged portfolios and the optimal hedge ratio and hedging effectiveness values for the given long position in US Dollar with the short position in Euro.

• 사상체질의학회지
• /
• 제8권1호
• /
• pp.101-186
• /
• 1996

1. 연구배경 : 사상의학의 가장 중요한 요점은 체질진단이다. 그간 다양한 체질변증에 관한 연구가 있었지만 신체 각부의 형태학적인 연구, 특히 얼굴을 대상으로 한 연구는 거의 전무하였다. 저자들은 그 동안 전일적이고 직관적으로 표현된 동의수세보원의 형태적 묘사를 정량화하여 정리하고, 이 자료를 체질진단의 근거자료로 삼고자 하는 연구의 일환으로 먼저 두안부(頭顔部)의 형태를 태음인 소음인 소양인 별로 그 형상적 특징을 찾아내고자 하였다. 2. 방법 : 1995년 7월부터 1995년 12월까지 경희의료원 부속한방병원 외래환자 및 직원을 대상으로 설문지 및 임상적 치료 경과를 통하여 체질적 경향성이 뚜렷한 대상자를 선별하고 동일촬영 조건을 통하여 얻은 얼굴 사진 중 형태특이자를 제외한 170례의 고경(전두고외 26항목) 방사경(두최대장외 22항목) 및 폭경(안최대폭외 18항목)등 총 69항목을 측정한 후 이를 분석하여 체질별 상이점을 도출하였다. 3. 결과 : 체질별 두면부의 형태학적인 특징을 수치화하여 설명할 수 있게 되었고, 나아가 직관적이고 전일적인 형태를 구체화시킬 수 있는 특징을 도출할 수 있었다. 4. 결론 : 이상의 결과를 이용하여 체질별 각 부분의 형태를 계량화하여 비교 설명하고, 이를 이용하여 체질판별공식을 만들었다.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제27권1호
• /
• pp.75-92
• /
• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• Communications for Statistical Applications and Methods
• /
• 제4권1호
• /
• pp.229-241
• /
• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• 한국통신학회논문지
• /
• 제38A권8호
• /
• pp.644-649
• /
• 2013

광기록 정보저장장치에서 인코딩된 시퀀스의 DC-억압을 위해 Guided Scrambling 기법이 널리 사용된다. 후보 코드시퀀스 중 최적의 DC-억압 코드를 선택하기 위해 digital sum value (DSV)의 함수로 정의된 기준을 사용한다. 이 중 minimum DSV (MDSV), minimum squared weight (MSW), minimum threshold overrun (MTO) 등이 널리 사용된다. 본 연구에서는 MDSV, MSW, MTO 기준을 채택하는 GS 코딩 알고리즘과 동등한 정수계획법 모형을 제안한다. 개발된 MDSV 정수계획법 모형을 MaxMin 형태의 모형으로 확장하여 스크램블링 다항식과 제어 비트에 따른 MDSV GS 코딩의 최악 성능을 평가할 수 있는 모형을 개발하였다. 모의실험에서는 다수의 스크램블링 다항식 및 제어비트 조합에 대하여 MDSV 최악 성능을 계산하였다.

• 대기
• /
• 제26권4호
• /
• pp.697-709
• /
• 2016

This study estimates and evaluates the extreme value of 30 m-resolution daily maximum and minimum temperatures over South Korea, using inverse distance weighting (IDW), parameter-elevation regression on independent slopes model (PRISM) and generalized extreme value (GEV) method. The three experiments are designed and performed to find the optimal estimation strategy to obtain extreme value. First experiment (EXP1) applies GEV firstly to automated surface observing system (ASOS) to estimate extreme value and then applies IDW to produce high-resolution extreme values. Second experiment (EXP2) is same as EXP1, but using PRISM to make the high-resolution extreme value instead of IDW. Third experiment (EXP3) firstly applies PRISM to ASOS to produce the high-resolution temperature field, and then applies GEV method to make high resolution extreme value data. By comparing these 3 experiments with extreme values obtained from observation data, we find that EXP3 shows the best performance to estimate extreme values of maximum and minimum temperatures, followed by EXP1 and EXP2. It is revealed that EXP1 and EXP2 have a limitation to estimate the extreme value at each grid point correctly because the extreme values of these experiments with 30 m-resolution are calculated from only 60 extreme values obtained from ASOS. On the other hand, the extreme value of EXP3 is similar to observation compared to others, since EXP3 produces 30m-resolution daily temperature through PRISM, and then applies GEV to that result at each grid point. This result indicates that the quality of statistically produced high-resolution extreme values which are estimated from observation data is different depending on the combination and procedure order of statistical methods.

• 한국군사과학기술학회지
• /
• 제2권2호
• /
• pp.271-278
• /
• 1999

An alternative panel flutter approach utilizing minimum angle is presented. The minimum angle is the lowest value among the angles between modes i and j at a certain pressure condition. This method utilizes eigenvectors rather than eigenvalues. Cross-ply composite plates are considered in this study. A remarkable result of this investigation is that the angle always dropped gradually to zero for all presented examples

• 의료ㆍ복지 건축 : 한국의료복지건축학회 논문집
• /
• 제23권1호
• /
• pp.15-24
• /
• 2017

Purpose: Korea is expected to enter an aged society in 2018 and then a super-aged society in early 2025. The country's aging is progressing faster than any other country in the world. However, the foundation of the elderly friendly industry is weak, and measures at the government level are urgently needed. Especially, housing problems of the elderly are one of the most urgent measures to be taken. Korea does not have the minimum residential area standard for the elderly, and the current general minimum residential area standard is based on the survey of the housing situation without scientific evidence. Therefore, both standards need to be revised as soon as possible based on scientific evidence. Methods: The minimum residential area standard has been calculated following Karl H. E. Kroemer's Min or Max design also being called as-single cut and dual cut theory- as the maximum population value and minimum population value theory of Ernest J. McCormick. Therefore there is a need for a formula made using a few key factors, such as corresponding dimension, practical dimension, clearance, spare dimension, integrated dimension. These elements can be defined and used as formulas to calculate minimum residential area standards. Results: Assuming the results of the spatial variability in this study showed that it is possible to raise the standard of living in a terms of sustainable minimum size for the young, old and all residents. Implications: The government should set a minimum residential area standard with scientific grounds and set up a policy improving the life of people who live in an needy residential environment.

• Steel and Composite Structures
• /
• 제37권4호
• /
• pp.463-479
• /
• 2020

Currently, there are many lateral resisting systems utilized in resisting lateral loads being produced in an earthquake. Such systems can significantly reduce the roof's displacement when placed at an optimum location. Since in the design of tall buildings, the minimum distance between adjacent buildings is important. In this paper, the critical excitation method is used to determine the best location of the belt truss system while calculating the minimum required distance between two adjacent buildings. For this purpose, the belt truss system is placed at a specific story. Then the critical earthquakes are computed so that the considered constraints are satisfied, and the value of roof displacement is maximized. This procedure is repeated for all stories; i.e., for each, a critical acceleration is computed. From this set of computed roof displacement values, the story with the least displacement is selected as the best location for the belt truss system. Numerical studies demonstrate that absolute roof displacements induced through critical accelerations range between 5.36 to 1.95 times of the San Fernando earthquake for the first example and 7.67 to 1.22 times of the San Fernando earthquake for the second example. This method can also be used to determine the minimum required distance between two adjacent buildings to eliminate the pounding effects. For this purpose, this value is computed based on different standard codes and compared with the results of the critical excitation method to show the ability of the proposed method.