• Korean Journal of Mathematics
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• 제23권1호
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• pp.1-10
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• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• Communications for Statistical Applications and Methods
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• 제26권4호
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.71-84
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• 2014

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H = 1/4.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제16권4호
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• pp.427-431
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• 2010

다차원 척도법(multidimensional scaling)은 고차원의 데이터를 낮은 차원의 공간에 매핑(mapping)하여 데이터 간의 유사성을 표현하는 방법이다. 이는 주로 자질 선정 및 데이터를 시각화하는 데 이용된다. 그러한 다차원 척도법 중, 전통 다차원 척도법(classical multidimensional scaling)은 긴 수행 시간과 큰 공간을 필요로 하기 때문에 객체의 수가 많은 경우에 대해 적용하기 어렵다. 이는 유클리드 거리(Euclidean distance)에 기반한 $n{\times}n$ 상이도 행렬(dissimilarity matrix)에 대해 고유쌍 문제(eigenpair problem)를 풀어야 하기 때문이다(단, n은 객체의 개수). 따라서, n이 커질수록 수행 시간이 길어지며, 메모리 사용량 증가로 인해 적용할 수 있는 데이터 크기에 한계가 있다. 본 논문에서는 이러한 문제를 완화하기 위해 GPGPU 기술 중 하나인 CUDA와 분할-정복(divide-and-conquer)기법을 활용한 효율적인 다차원 척도법을 제안하며, 다양한 실험을 통해 제안하는 기법이 객체의 개수가 많은 경우에 매우 효율적일 수 있음을 보인다.

• 천문학회보
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• 제36권2호
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• pp.106.2-106.2
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• 2011

The two competing theories of star formation are based on turbulence and ambipoar diffusion. I will first briefly explain the two theories. There have been analytical (or semi-analytic) models, which estimate star formation rates in a turbulent cloud. Most of them are based on the log-normal density PDF (probability density function) of the turbulent cloud without self-gravity. I will first show that the core (star) formation rate can be increased significantly once self-gravity of a turbulence cloud is taken into account. I will then present the evolution of molecular line profiles of HCO+ and C18O toward a dense core that is forming inside a magnetized turbulent molecular cloud. Features of the profiles can be affected more significantly by coupled velocity and abundance structures in the outer region than those in the inner dense part of the core. During the evolution of the core, the asymmetry of line profiles easily changes from blue to red, and vice versa. Finally, I will introduce a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamic code.