• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.79-84
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• 2003

Likelihood estimation in random-effect models is often complicated because the marginal likelihood involves an analytically intractable integral. Numerical integration such as Gauss-Hermite quadrature is an option, but is generally not recommended when the dimensionality of the integral is high. An alternative is the use of hierarchical likelihood, which avoids such burdensome numerical integration. These two approaches for fitting binary data are compared and the advantages of using the hierarchical likelihood are discussed. Random-effect models for binary outcomes and for bivariate binary-continuous outcomes are considered.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.177-193
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• 2022

The main aim of this paper is to introduce a new generalization of the Wright series in two variables, which is expressed in terms of Hermite polynomials. The properties of the freshly defined function involving its auxiliary functions and the integral representations are established. Furthermore, a Gauss-Hermite quadrature and Gaussian quadrature formulas have been established to evaluate some integral representations of our main results and compare them with our theoretical evaluations using graphical simulations.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.957-981
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• 2017

A generalized linear mixed model is an extension of a generalized linear model that allows random effect as well as provides flexibility in developing a suitable model when observations are correlated or when there are other underlying phenomena that contribute to resulting variability. We describe maximum likelihood estimation methods for logistic regression models that include random effects - the Laplace approximation, Gauss-Hermite quadrature, adaptive Gauss-Hermite quadrature, and pseudo-likelihood. Applications are provided with social science problems by analyzing the effect of mental health and life satisfaction on volunteer activities from Korean welfare panel data; in addition, we observe that the inclusion of random effects in the model leads to improved analyses with more reasonable inferences.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.315-323
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• 2019

Panel data sets have recently been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Often a dichotomous dependent variable occur in survival analysis, biomedical and epidemiological studies that is analyzed by a generalized linear mixed effects model (GLMM). The most common estimation method for the binary panel data may be the maximum likelihood (ML). Many statistical packages provide ML estimates; however, the estimates are computed from numerically approximated likelihood function. For instance, R packages, pglm (Croissant, 2017) approximate the likelihood function by the Gauss-Hermite quadratures, while Rchoice (Sarrias, Journal of Statistical Software, 74, 1-31, 2016) use a Monte Carlo integration method for the approximation. As a result, it can be observed that different packages give different results because of different numerical computation methods. In this note, we discuss the pros and cons of numerical methods compared with the exact computation method.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.673-679
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• 2021

The moment calculation in a truncated multivariate normal distribution is a long-standing problem in statistical computation. Recently, Kan and Robotti (2017) developed an algorithm able to calculate all orders of moment under different types of truncation. This result was implemented in an R package MomTrunc by Galarza et al. (2021); however, it is difficult to use the package in practical statistical problems because the computational burden increases exponentially as the order of the moment or the dimension of the random vector increases. Meanwhile, Lee (2021) presented an efficient numerical method in both accuracy and computational burden using Gauss-Hermit quadrature. This article introduces trunmnt implementation of Lee's work as an R package. The Package is believed to be useful for moment calculations in most practical statistical problems.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.69-72
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• 2005

In this paper, pseudo noise (PN) code acquisition performance with multiple antennas in a UWB time hopping/code division multiple access system is analyzed. The closed form for the conditional probability is derived, using the Gauss-Hermite quadrature formula, when the signal with Gaussian distribution goes through the lognormal fading channel. The performance comparison of the above mentioned schemes shows that the code acquisition performance with a diversity combining technique, especially when increasing the number of antennas, is more robust than that using no diversity.

• Nuclear Engineering and Technology
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• v.50 no.3
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• pp.340-355
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• 2018

The methods and performance of a fast reactor multigroup cross section (XS) generation code EXUS-F are described that is capable of directly processing Evaluated Nuclear Data File format nuclear data files. RECONR of NJOY is used to generate pointwise XS data, and Doppler broadening is incorporated by the Gauss-Hermite quadrature method. The self-shielding effect is incorporated in the ultrafine group XSs in the resolved and unresolved resonance ranges. Functions to generate scattering transfer matrices and fission spectrum matrices are realized. The extended transport approximation is used in zero-dimensional calculations, whereas the collision probability method and the method of characteristics are used for one-dimensional cylindrical geometry and two-dimensional hexagonal geometry problems, respectively. Verification calculations are performed first for various homogeneous mixtures and cylindrical problems. It is confirmed that the spectrum calculations and the corresponding multigroup XS generations are performed adequately in that the reactivity errors are less than 50 pcm with the McCARD Monte Carlo solutions. The nTRACER core calculations are performed with the EXUS-F-generated 47 group XSs for the two-dimensional Advanced Burner Reactor 1000 benchmark problem. The reactivity error of 160 pcm and the root mean square error of the pin powers of 0.7% indicate that EXUF-F generates properly the broad-group XSs.