• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.743-752
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• 2004

In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.

• Journal of the Korean Statistical Society
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• 제33권1호
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• pp.129-147
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• 2004

For square contingency tables with nominal categories, this paper proposes a measure to represent the degree of departure from the quasi-symmetry (QS) model and the Bradley-Terry (BT) model. The measure proposed is expressed by using the Cressie and Read (1984)'s power-divergence or Patil and Taillie (1982)'s diversity index. The measure lies between 0 and 1, and it is useful for comparing the degree of departure from QS or BT in several tables.

• Journal of the Korean Statistical Society
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• 제27권3호
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• pp.289-303
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• 1998

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.

• Communications for Statistical Applications and Methods
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• 제10권1호
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• pp.135-144
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• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Journal of the Korean Data and Information Science Society
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• 제17권2호
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.289-301
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• 1996

This paper suggests a new diagnostic measure for detecting influential observations in two group linear discriminant analysis(LDA). It is developed from an information theoretic point of view using the minimum discrimination information(MDI) methodology. MDI estimator of symmetric divergence by Kullback(l967) is taken as a measure of the power of discrimination in LDA. It is shown that the effect of an observation over the power of discrimination is fully explained by the diagnostic measure. Asymptotic distribution of the proposed measure is derived as a function of independent chi-squared and standard normal variables. By means of the distributions, a couple of methods are suggested for detecting the influential observations in LDA. Performance of the suggested methods are examined through a simulation study.

• 응용통계연구
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• 제16권2호
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• pp.455-467
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• 2003

소표본 분할표 자료에서 적합도 검정통계량들의 카이제곱 근사 적용 가능에 대하여 많은 연구가 진행되었다. 소표본에서 세 가지 검정 통계량(피어슨 카이제곱 Χ$^2$, 일반화 가능도비 G$^2$, 그리고 역발산 Ι(2/3) 검정통계량)에 관하여 비교한 Rudas(1986)의 연구를 확장하여, 최근에 제안된 차이측도(BWHD(1/9), BWCS(1/3), NED(4/3) 검정통계량)를 포함시켜 비교 분석하였다. 독립모형의 이차원 분할표, 조건부 독립모형과 한 변수 독립 모형을 따르는 삼차원 분할표에 대한 모의실험을 통하여 생성된 90과 95 백분위수와 이에 대응하는 95% 신뢰구간을 살펴보고 실제 백분위수와 비교하였다. 그 결과 Χ$^2$, Ι(2/3), 그리고 BWHD(1/9) 검정통계량이 유사한 결과를 나타내었고 이 통계량들이 기존에 제안된 검정통계량들보다 적은 표본크기에서도 카이제곱 근사방법에 적용 가능함을 발견하였다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2008년도 추계학술대회 논문집 Vol.21
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• pp.368-368
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• 2008

Ion implantation has been widely developed during the past decades to become a standard industrial tool. To comply with the growing needs in ion implantation, innovative technology for the control of ion beam parameters is required. Beam current, beam profile, ion fractions are of great interest when uniformity of the implant is an issue. Especially, it is important to measure the spatial distribution of beam power and also the energy distribution of accelerated ions. This energy distribution is influenced by the proportion of mass for ion in the plasma generator(ion source) and by charge exchange and dissociation within the accelerator structure and also by possible collective effects in the neutralizer which may affect the energy and divergence of ions. Hydrogen atom has been the object of a good study to investigate the energy distribution. Hydrogen ion sources typically produce multi-momentum beams consisting of atomic ion ($H^+$) and molecular ion ($H_2^+$ and $H_3^+$). In the beam injector, the molecular ions pass through a charge-exchanges gas cell and break up into atomic with one-half (from $H_2^+$) or one-third (from $H_3^+$) according to their accelerated energy. Burrell et al. have observed the Doppler shifted lines from incident $H^+$, $H_2^+$, and $H_3^+$ using a Doppler shift spectroscopy. Several authors have measured the proportion of mass for hydrogen ion and deuterium using an ion source equipped with a magnetic dipole filter. We developed an ion implanter with 50-KeV and 20-mA ion source and 100-keV accelerator tube, aiming at commercial uses. In order to measure the proportion of mass for ions, we designed a filter system which can be used to measure the ion fraction in any type of ion source. The hydrogen and helium ion species compositions are used a filter system with the two magnets configurations.

• 자원ㆍ환경경제연구
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• 제23권1호
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• pp.43-65
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• 2014

본 논문에서는 국내 제조업 가운데 전력 사용량이 상대적으로 많은 화합물 및 화학제품 산업을 대상으로 암묵 (shadow) 비용함수를 사용하여 전력 등의 투입요소 간 효율적 배분 여부를 검증하고 전력의 적정수준 대비 과잉 투입 규모를 조사한다. 기업의 비용최소화 달성을 전제로 각 투입요소에 대한 수요의 가격탄력성을 추정하여 전력요금 인상에 대한 각 요소 수요의 파급효과를 모의실험을 통하여 분석한다. 또한 공급관계식을 비용함수의 방정식체계에 추가하여 동시 추정함으로써 전력요금 10% 인상 시 물가지수에 미치는 영향을 분석한다. 실증분석 결과, 1982-2006년 기간 동안 '투입요소 간 효율적 배분 달성'의 귀무가설은 기각되었으며, 전력은 적정수준 대비 평균적으로 매년 약 98% 과잉 사용되고 있는 것으로 나타났다. 다른 요인들이 불변하다면 전력요금이 10% 인상될 경우 전력 수요는 약 11.4% 감소하였으며, 공급가격은 평균적으로 0.08% 하락하는 것으로 나타났다.