• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.799-808
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• 2011

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{\mid}1{\leq}i{\leq}n$} is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{\mathcal{F}}$ (f($X_1$, ${\ldots}$, $X_n$), g($X_1$, ${\ldots}$, $X_n$)) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$-associated random variables.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.543-558
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• 2006

We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.225-231
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• 1995

An eventual uniform equicontinuity condition is investigated in the context of the uniform central limit theorem (UCLT) for continuous martingales. We assume the usual intergrability condition on metric entropy. We establish an exponential inequality for a martingales. Then we use the chaining lemma of Pollard (1984) to prove an eventual uniform equicontinuity which is a sufficient condition of UCLT. We apply the result to approximate a stochastic integral with respect to a martingale to that of a Brownian motion.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• Journal of Preventive Medicine and Public Health
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• v.55 no.4
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• pp.389-397
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• 2022

Objectives: This study examined the effect of out-of-pocket (OOP) payment reduction on the potential utilization of low-value magnetic resonance imaging (MRI) across income groups. Methods: We conducted an experimental vignette survey using a proportional quota-based sample of individuals in Korea (n=1229). In two hypothetical vignettes, participants were asked whether they would be willing to use MRI if they had uncomplicated headache and non-specific low back pain, each before and after OOP payment reduction. To account for the possible role of physician inducement, half of the participants were initially presented with vignettes that included a physician recommendation for low-value care. The predicted probability, slope index of inequality (SII), and relative index of inequality (RII) were calculated using logistic regression. Results: Before OOP payment reduction, the lowest income quintile was least likely to use low-value MRI regardless of physician inducement (36.7-49.6% for low back pain; 30.5-39.3% for headache). After OOP payment reduction, almost all individuals in each income quintile were willing to use low-value MRI (89.8-98.0% for low back pain; 78.1-90.3% for headache). Absolute and relative inequalities concerning potential low-value MRI utilization decreased after OOP payments were reduced, even without physician inducement (SII: from 8.15 to 5.37%, RII: from 1.20 to 1.06 for low back pain; SII: from 6.99 to 0.83%, RII: from 1.20 to 1.01 for headache). Conclusions: OOP payment reduction for MRI has the potential to increase low-value care utilization among all income groups while decreasing inequality in low-value care utilization.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.5
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• pp.219-225
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• 2017

This article examined the condition of medical service utilization and the usage degree for the disabled in Korea, and analyzed factors affecting medical service utilization. This paper offers data for improving the health of disabled Korea residents and for enhancing medical service utilization. We analyzed data for disabled residents aged 19 from the 6th Korea National Health and Nutrition Examination Survey. Results found significant effects depending on gender, age, average monthly income, types of disorders, disability rating, and status of smoking. Concerning gender, men had a higher probability of lacking medical treatment compared with women, had increased probability of having a disability, and smokers had a higher probability of lacking treatment compared with nonsmokers. Therefore, for resolving medically untreated disabled Korean residents, government needs to improve the policy system and to managethe inequality of handicapped welfare work.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.5
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• pp.458-463
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• 2004

This paper presents a fast IA(integer ambiguity) resolution method that determines the IA within short epochs with guaranteed reliability. Based on the fact that the search volume and the cost function are influenced by the selection of primary IAs in the plane intersection method, an IA resolution method is proposed that evaluates IA candidates repeatedly in an epoch with different combinations of primary IAs. In order to guarantee the reliability of the resolved IA with a certain probability, an inequality condition for selecting differencing operator is derived. Experiment results show that the proposed method consistently provides the true IA estimates within short time.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.317-328
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• 2014

In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.95-102
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• 2003

To define an analytical model for a structural system or to assess damage in the system, system identification(SI) methods have been developed and widely applied. The paper presents a method of determining optimal sensor location(OSL) based on the maximum likelihood approach, which is applicable to modal SI methods. To estimate unknown parameters reliably, it is necessary that the information provided by the experiment should be maximized. By applying the Cramer-Rao inequality, a Fisher information matrix in terms of the probability density function of measurements is obtained from a lower bound of the estimation error. The paper also proposes a scheme of determining of OSL on damaged structures by using maximum strain energy factor. Simulation studies have carried out to investigate the proposed OSL algorithm for both undamaged and damaged structures.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.