• Communications for Statistical Applications and Methods
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• 제25권6호
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• pp.633-645
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• 2018

Gaussian error distributions are a common choice in traditional regression models for the maximum likelihood (ML) method. However, this distributional assumption is often suspicious especially when the error distribution is skewed or has heavy tails. In both cases, the ML method under normality could break down or lose efficiency. In this paper, we consider the log-concave and Gaussian scale mixture distributions for error distributions. For the log-concave errors, we propose to use a smoothed maximum likelihood estimator for stable and faster computation. Based on this, we perform comparative simulation studies to see the performance of coefficient estimates under normal, Gaussian scale mixture, and log-concave errors. In addition, we also consider real data analysis using Stack loss plant data and Korean labor and income panel data.

• Communications for Statistical Applications and Methods
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• 제29권6호
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• pp.641-653
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• 2022

Penalized least squares methods are important tools to simultaneously select variables and estimate parameters in linear regression. The penalized maximum likelihood can also be used for the same purpose assuming that the error distribution falls in a certain parametric family of distributions. However, the use of a certain parametric family can suffer a misspecification problem which undermines the estimation accuracy. To give sufficient flexibility to the error distribution, we propose to use the symmetric log-concave error distribution with LASSO penalty. A feasible algorithm to estimate both nonparametric and parametric components in the proposed model is provided. Some numerical studies are also presented showing that the proposed method produces more efficient estimators than some existing methods with similar variable selection performance.

• 대한수학회보
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• 제51권2호
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• pp.539-545
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• 2014

We show that roots of log-concave Alexander knot polynomials are dense in C. This in particular implies that the log-concavity and Hoste's conjecture on the Alexander polynomial of alternating knots are (essentially) independent.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.593-610
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• 2015

적응 기각 추출 (adaptive rejection sampling)방법은 특정한 형태의 확률분포로 부터 확률표본을 추출하기 위한 대표적인 난수생성기 (random number generator)로서, 추출된 표본으로부터 제안분포 (proposal distribution)가 개선이 되는 장점을 가지고 있다. 그러나, 기존에 제안된 적응기각추출 방법은 확률분포의 형태가 로그-오목 함수 (log-concave function)인 경우에만 사용이 가능하기 때문에 적용범위가 제한적이다. 최근의 연구결과에서는, 이러한 단점을 보완하기 위해 다양한 형태의 적응기각추출이 진행되고 있으며, 이에 본 논문에서는 기존의 적응기각추출 방법을 포함한 총 5가지의 난수 생성 방법에 대해서 고찰하고, 아울러 모의실험을 통해 각 방법들간의 성능에 대하여, 적합성과 효율성의 관점에서 실증적으로 비교 분석하도록 한다.

• Bulletin of the Korean Chemical Society
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• 제32권3호
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• pp.857-862
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• 2011

Kinetic studies of the reactions of N-methyl-Y-${\alpha}$-bromoacetanilides with substituted X-benzylamines have been carried out in dimethyl sulfoxide at $25.0^{\circ}C$. The Hammett plots for substituent X variations in the nucleophiles (log $k_N$ vs ${\sigma}_X$) are slightly biphasic concave upwards/downwards, while the Bronsted plots (log $k_N$ vs $pK_a$) are biphasic concave downwards with breakpoints at X = H. The Hammett plots for substituent Y variations in the substrates (log $k_N$ vs ${\sigma}_Y$) are biphasic concave upwards/downwards with breakpoints at Y = H. The cross-interaction constant $\rho_{XY}$ values are all negative: $\rho_{XY}$ = -0.32 for X = Y = electron-donating; -0.22 for X = electron-withdrawing and Y = electron-donating; -1.80 for X = electron-donating and Y = electronwithdrawing; -1.43 for X = Y = electron-withdrawing substituents. Deuterated kinetic isotope effects are primary normal ($k_H/k_D$ > 1) for Y = electron-donating, while secondary inverse ($k_H/k_D$ < 1) for Y = electronwithdrawing substituent. The proposed mechanisms of the benzylaminolyses of N-methyl-Y-${\alpha}$-bromoacetanilides are a concerted mechanism with a five membered ring TS involving hydrogen bonding between hydrogen (deuterium) atom in N-H(D) and oxygen atom in C = O for Y = electron-donating, while a concerted mechanism with an enolate-like TS in which the nucleophile attacks the ${\alpha}$-carbon for Y = electronwithdrawing substituents.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2012년도 한국컴퓨터종합학술대회논문집 Vol.39 No.1(D)
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• pp.219-221
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• 2012

The concave utility in the Network Utility Maximization (NUM) problem is only suitable for elastic flows. In networks with multiclass traffic, the utility can be concave, linear, step or sigmoidal. Hence, the basic NUM becomes a nonconvex optimization problem. The current approach utilizes the standard dual-based decomposition method. It does not converge in case of scarce resource. In this paper, we propose an algorithm that always converges to a local optimal solution to the nonconvex NUM after solving a series of convex approximation problems. Our techniques can be applied to any log-concave utilities.

• Bulletin of the Korean Chemical Society
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• 제32권10호
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• pp.3587-3591
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• 2011

The reactions of O,O-diethyl Z-S-aryl phosphorothioates with X-benzylamines are kinetically investigated in dimethyl sulfoxide at $85.0^{\circ}C$. The Hammett (log $k_2$ vs ${\sigma}x$) and Br$\ddot{o}$nsted [log $k_2$ vs $pK_a$(X)] plots are biphasic concave downwards for substituent X variations in the nucleophiles with a break point at X = H. The signs of the cross-interaction constants (${\rho}xz$) are positive for both the strongly and weakly basic nucleophiles. Considerably great magnitude of ${\rho}xz$ (= 6.56) value is observed with the weakly basic nucleophiles, while ${\rho}xz$ = 0.91 with the strongly basic nucleophiles. Proposed reaction mechanism is a stepwise process with a rate-limiting leaving group expulsion from the intermediate involving a backside nucleophilic attack with the strongly basic nucleophiles and a frontside attack with the weakly basic nucleophiles. The kinetic results are compared with those of the benzylaminolysis of O,O-diphenyl Z-S-aryl phosphorothioates.

• 대한수학회논문집
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• 제14권3호
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2008년도 추계 학술발표회
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• pp.1081-1089
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• 2008

Highly plastic clays in their normally consolidated state are not linear but are concave upwards. Thus their compression index deceases with the increase in consolidation pressure. Likeness the e - log ${\sigma}\;_{\upsilon}\;'$ curves of the silts are not linear but are convex upwards. In this paper, conducted consolidation test with four undisturbed field soil and found that their e - log ${\sigma}\;_{\upsilon}\;'$ plots are not linear. And analyzed difference of settlement between computed value with compression index($C_c$) and computed value with improved compression index($\mathbb{C}$).

• 한국항해항만학회지
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• 제36권3호
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• pp.181-187
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• 2012

고소성 점토 및 소성, 비소성 실트의 정규압밀상태시의 처녀압축곡선이 항상 선형적 거동을 하는 것은 아니며, 비선형성을 가진 한국의 남해안 점토의 경우 압밀압력이 증가함에 따라 압축지수가 감소하며, $e-{\log}{\sigma}_{\upsilon}{\prime}$곡선은 아래로 오목한 형태의 거동을 하는 것으로 연구되었다. 본 연구에서는 한국 남부 해안의 점토를 대상으로 압밀시험을 수행하였고, 결과를 분석하여 초기간극비, 액성한계, 소성지수와 압축지수의 비선형성을 분석하였다. Butterfield의 기법을 이용한 ${\ln}{\upsilon}-{\ln}{\sigma}_{\upsilon}{\prime}$에서 액성한계 50~100%사이의 처녀압축곡선은 선형성을 보였으나, 초기간극비 2.24%, 액성한계 100%, 소성지수 60이상에서의 고소성 점토의 시험결과에서는 뚜렷한 비선형성이 나타났다. 비소성 실트(fly ash)를 90%이상 함유한 재성형 시료의 경우 압밀압력이 증가함에 따라 압축지수가 증가하는 경향을 보였다.