• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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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.

• 대한수학회논문집
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• 제37권1호
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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.

• 응용통계연구
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• 제30권6호
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• pp.957-981
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• 2017

관측되지 않는 효과 또는 고정효과로 설명할 수 없는 분산 구조가 포함되어 정확한 모수 추정이 어려운 경우 체계적인 분석을 위해 일반화 선형 모형은 임의효과가 포함된 일반화 선형 혼합 모형으로 확장되었다. 본 연구에서는 일반화 선형 모형 중에서도 이분적인 반응변수를 다루는 로지스틱 회귀모형에 임의효과를 포함한 최대 우도 추정 방법을 설명한다. 그중에서도 라플라스 근사법, 가우스-에르미트 구적법, 적응 가우스-에르미트 구적법 그리고 유사가능도 우도에 대한 최대우도 추정법을 자세히 알아본다. 또한 제안한 방법을 사용하여 한국 복지 패널 데이터에서 정신건강과 생활만족도가 자원봉사활동에 미치는 영향에 대해 분석한다.

• Communications for Statistical Applications and Methods
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• 제26권3호
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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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• 제28권6호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2005년도 추계종합학술대회
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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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• 제50권3호
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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.