• Communications for Statistical Applications and Methods
• /
• v.25 no.6
• /
• pp.633-645
• /
• 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
• /
• v.29 no.6
• /
• pp.641-653
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.3
• /
• pp.593-610
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.627-633
• /
• 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.

• The Korean Journal of Applied Statistics
• /
• v.16 no.2
• /
• pp.273-282
• /
• 2003

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

• Journal of the Korean earth science society
• /
• v.38 no.7
• /
• pp.511-521
• /
• 2017

This study analyzes Two-dimensional video disdrometer (2DVD) data while summer 2011-2012 in Daegu region and compares with Marshall and Palmer (MP) distribution to find out statistical characteristics and characteristics variability about drop size distribution (DSD) of Daegu region. As the characterize DSD of Daegu region, this study uses single moment parameters such as rainfall intensity (R), reflectivity factor (Z) and double moment parameters such as generalized characteristics number concentration ($N{_0}^{\prime}$) and generalized characteristics diameter ($D{_m}^{\prime}$). Also, this study makes an assumption that DSD function can be expressed as general gamma distribution. The results of analysis show that DSD of Daegu region has ${\log}_{10}N{_0}^{\prime}=2.37$, $D{_m}^{\prime}=1.04mm$, and c =2.37, ${\mu}=0.39$ on average. When the assumption of MP distribution is used, these figures then end up with the different characteristics; ${\log}_{10}N{_0}^{\prime}=2.27$, $D{_m}^{\prime}=0.9mm$, c =1, ${\mu}=1$ on average. The differences indicate liquid water content (LWC) of Daegu distribution is generally larger than MP distribution at equal Z. Second, DSD shape of Daegu distribution is concave upward. Other important facts are the characteristics of Daegu distribution change when Z changes. DSD shape of Daegu region changes concave downward (c =2.05~2.55, ${\mu}=0.33{\sim}0.77$) to cubic function-like shape (c =3.0, ${\mu}=-0.13{\sim}-0.33$) at Z > 45 dBZ. 35 dBZ ${\leq}$ Z > 45 dBZ group of Daegu distribution has characteristics similar to maritime cluster of diverse climate DSD study. However, Z > 45 dBZ group of Daegu distribution has a difference from the cluster.

• Geophysics and Geophysical Exploration
• /
• v.17 no.1
• /
• pp.28-33
• /
• 2014

We investigate the spatial distribution of highly conductive layer using the one-dimensional inversions of the new magnetotelluric (MT) measurements obtained at the mid-mountain (400 ~ 900 m in elevation) western area of Jeju Island and the previous MT data over Jeju Island, Korea. The conductive layer indicates the sedimentary layer comprised of Seoguipo Fomation and U Formation. There is a definite positive correlation between the top of conductive layer and the earth surface in elevation. On the contrary, the bottom of conductive layer has a negative correlation with the surface elevation. In other words, the conductive layer has a shape of convex lens, which is thickest in the central part. The basement beneath the conductive layer could be concave in the central part of Jeju Island. A kriging considering the correlation between the layer boundary and the surface elevation provides a reliable geoelectric structure model of Jeju Island. However, further studies, i.e. three-dimensional modeling and interpretation integrated with other geophysical or logging data, are required to reveal the possible presence of three-dimensional conductive body near the subsurface vent of Mt. Halla and the causes of the bias in the depths of layer estimated from MT and core log data.