• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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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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• v.33 no.1
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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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• v.27 no.3
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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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• v.10 no.1
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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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• v.17 no.2
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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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• v.25 no.2
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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.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.455-467
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• 2003

There has been a long debate on the applicability of the chi-square approximation to statistics based on small sample size. Extending comparison results among Pearson chi-square Χ$^2$, generalized likelihood .ratio G$^2$, and the power divergence Ι(2/3) statistics suggested by Rudas(1986), recently developed disparity statistics (BWHD(1/9), BWCS(1/3), NED(4/3)) we compared and analyzed in this paper. By Monte Carlo studies about the independence model of two dimension contingency tables, the conditional model and one variable independence model of three dimensional tables, simulated 90 and 95 percentage points and approximate 95% confidence intervals for the true percentage points are obtained. It is found that the Χ$^2$, Ι(2/3), BWHD(1/9) test statistics have very similar behavior and there seem to be applcable for small sample sizes than others.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.11a
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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.

• Environmental and Resource Economics Review
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• v.23 no.1
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• pp.43-65
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• 2014

In this paper, we test for allocative efficiency of productive inputs including electricity and measure the divergence between the actual and optimal level of electricity for the chemical products, which is a relatively highly electricity-intensive sector in Korean manufacturing industries, by estimating a shadow cost function. Supposing cost minimization subject to market prices was achieved, we derive the price elasticities of demand for each input and simulate the impact of a 10% increase in power rate on its demand and supply price by estimating jointly a cost function with an inverse supply relation. The null hypothesis of allocative efficiency of inputs is rejected over the period 1982-2006. On average, electricity is used more than optimal level by 98% per year. The demand for electricity decreases by 11.4%, and supply price, on average, falls by 0.08%, other things being equal.