• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.41-61
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• 2001

The minimum negative exponential disparity estimator(MNEDE), introduced by Lindsay(1994), is an excellenet competitor to the minimum Hellinger distance estimator(Beran 1977) as a robust and yet efficient alternative to the maximum likelihood estimator in parametric models. In this paper we define the negative exponential deviance test(NEDT) as an analog of the likelihood ratio test(LRT), and show that the NEDT is asymptotically equivalent to he LRT at the model and under a sequence of contiguous alternatives. We establish that the asymptotic strong breakdown point for a class of minimum disparity estimators, containing the MNEDE, is at least 1/2 in continuous models. This result leads us to anticipate robustness of the NEDT under data contamination, and we demonstrate it empirically. In fact, in the simulation settings considered here the empirical level of the NEDT show more stability than the Hellinger deviance test(Simpson 1989). The NEDT is illustrated through an example data set. We also define a goodness-of-fit statistic to assess adequacy of a specified parametric model, and establish its asymptotic normality under the null hypothesis.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.2
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• pp.63-70
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• 2022

Although 2D Object detection has been largely improved in the past years with the advance of deep learning methods and the use of large labeled image datasets, 3D object detection from 2D imagery is a challenging problem in a variety of applications such as robotics, due to the lack of data and diversity of appearances and shapes of objects within a category. Google has just announced the launch of Objectron that has a novel data pipeline using mobile augmented reality session data. However, it also is corresponding to 2D-driven 3D object detection technique. This study explores more mature 2D object detection method, and applies its 2D projection to Objectron 3D lifting system. Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a stochastic representation of object regions using Gaussian distributions. We also present a similarity measure for the Gaussian distributions based on the Hellinger Distance, which can be viewed as a stochastic Intersection-over-Union. Our experimental results show that the proposed Gaussian representations are closer to annotated segmentation masks in available datasets. Thus, less accuracy problem that is one of several limitations of Objectron can be relaxed.

• 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.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.149-167
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• 2005

The minimum disparity estimators introduced by Lindsay and Basu (1994) are studied empirically. An extensive simulation in this paper provides a location estimate of the small sample and supplies empirical evidence of the estimator performance for the univariate contaminated normal model. Empirical results show that the minimum generalized negative exponential disparity estimator (MGNEDE) obtains high efficiency for small sample sizes and dominates the maximum likelihood estimator (MLE) and the minimum blended weight Hellinger distance estimator (MBWHDE) with respect to efficiency at the contaminated model.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.911-915
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• 1997

The purpose of this paper is to consider the problem of selection of optimal smoothing parameter for kernel-type distribution function estimator, which asymptotically minimizes mean Hellinger distance.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.347-366
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• 2001

Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions. The test statistics are generalizations of the Hellinger deviance test of Simpson(1989) and disparity tests of Lindsay(1994), obtained by looking at a 'penalized' version of the distances; harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells. The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test. Also, the tests based on the penalized distances are improvements over those based on the ordinary distances in that they are much closer to the likelihood ratio tests at the null and their convergence to the x$^2$ distribution appears to be dramatically faster; extensive simulation results show that the improvement in performance of the tests due to the penalty is often substantial in small samples.

• Korean Journal of Ecology and Environment
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• v.52 no.3
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• pp.274-283
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• 2019

Beta diversity is an efficient means of assessing the spatial variation in community composition among sites. To present fish community variation and LCBD (Local Contribution to Beta Diversity) among sites in stream, 6 sampling sites were selected in Cheonggye stream. Fish communities, environmental and habitat variables were collected at sites from April 2014 to October 2015. We used the total variance of the fish community data table (site-by-species community table) based on different forms, presence-absence, abundance, and Hellinger transformation, to estimate and compare beta diversity and LCBD. Fish community data table transformed by Hellinger distance showed the higher values of beta diversity than presence-absence and abundance data table. A similar patterns of LCBD were observed with presence-absence and Hellinger transformed data table. Low value of beta diversity calculated by community data table with abundance was due to the non-normality of fish assemblage data. Additionally, correlation coefficients were calculated to evaluate the relationships among LCBD, community indices and physicochemical variables. LCBD showed negative correlation coefficients with Shannon diversity. Overall, application of beta diversity analysis is an efficient method of addressing spatial variation of fish communities and ecological uniqueness of the sites in stream.

• 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.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.135-140
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• 2004

Lindsay and Basu (1994)에 의해 소개된 최소차이추정량 (Minimum Disparity Estimators)들은 실제 자료 분석 도구로써 유용하다. 본 논문에서는 최소일반화음지수 차이추정량 (Minimum Generalized Negative Exponential Disparity Estimator, MGNEDE)이 최대가능도추정량 (Maximum Likelihood Estimator, MLE)와 최소가중 헬링거거리추정량 (Minimum Blended Weight Hellinger Distance Estimator, MBWHDE)에 비해 오염된 정규모형에서 효율적이고 로버스트하다는 것을 모의실험을 통하여 확인하였다. 또한 세 가지 추정량들에 의해 추정된 모수들을 이용하여 판별하였을 때 자 추정량득의 판별율을 비교함으로써 오염된 정규모형에서 MLE의 대안으로 MGNEDE와 MBWHDE를 사용할 수 있음을 보였다.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.3 no.2
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• pp.122-128
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• 2022

To present the spatial variation of fish assemblages in the Geum River in Korea, the concept of beta diversity (β-diversity) estimates based on the variance of the community data table was applied. Fish communities and environmental variables were collected from 13 sampling sites along the in mid-low reaches of the River. We calculated the β-diversity and local contribution to beta diversity (LCBD) values at each site depending on the two types of data, 'occurrence' with Jaccard and Sørensen dissimilarity coefficients, and 'abundance' with Hellinger distance. Multivariate and correlation analyses were also performed to determine the relationships between LCBD and other variables, such as community indices and physicochemical and hydrological factors. The β-diversity values of fish communities in the River were estimated as 0.218 and 0.145 for occurrence data table with Jaccard and Sørensen respectively, and 0.268 for abundance data. Similar patterns of LCBD along the sampling sites were detected in two dissimilarity measurements of occurrence table, and LCBD values with abundance data were slightly different. The LCBD values are strongly correlated with community indices, and also suitable for indicating the uniqueness of fish assemblages. However, further research is needed to determine the LCBD value as an indicator of environmental variability.