• Communications for Statistical Applications and Methods
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• v.25 no.6
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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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• v.29 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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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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• v.26 no.3
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• pp.593-610
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• 2015

Adaptive Rejection Sampling (ARS) method is a well-known random number generator to acquire a random sample from a probability distribution, and has the advantage of improving the proposal distribution during the sampling procedures, which update it closer to the target distribution. However, the use of ARS is limited since it can be used only for the target distribution in the form of the log-concave function, and thus various methods have been proposed to overcome such a limitation of ARS. In this paper, we attempt to compare five random number generators based on ARS in terms of adequacy and efficiency. Based on empirical analysis using simulations, we discuss their results and make a comparison of five ARS-based methods.

• Bulletin of the Korean Chemical Society
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• v.32 no.3
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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.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06d
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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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• v.32 no.10
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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.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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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.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.10a
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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($\mathbb{C}$).

• Journal of Navigation and Port Research
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• v.36 no.3
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• pp.181-187
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• 2012

Highly plastic clays in their normally consolidated states are not always linear but are concave downwards. Thus their compression index deceases with the increase of consolidation pressure. The $e-{\log}{\sigma}_{\upsilon}{\prime}$ curves of plastic or non-plastic silty clays are not linear but are convex upwards. In this paper, consolidation tests were conducted with several undisturbed field soils of Korea south coast and their $e-{\log}{\sigma}_{\upsilon}{\prime}$ plots are not always linear. In case of using Butterfield's method(liquid limit 50~100%), ${\ln}{\upsilon}-{\ln}{\sigma}_{\upsilon}{\prime}$ plots are linear. But some undisturbed samples which have void ratio over 2.24, liquid limit over 100% and plasticity index over 60% are not linear. In results of consolidation tests with remolded samples which contain silt(fly ash) contents of 90% has compression index increasing with the increase in consolidation pressure.