• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.377-386
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• 2004

A technique that provides prediction intervals based on a model called an empirical linear model is discussed. The technique, high-dimensional empirical linear prediction (HELP), involves principal component analysis, factor analysis and model selection. HELP can be viewed as a technique that provides prediction (and confidence) intervals based on a factor analysis models do not typically have justifiable theory due to nonidentifiability, we show that the intervals are justifiable asymptotically.

• Earthquakes and Structures
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• v.25 no.6
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• pp.429-442
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• 2023

To study the seismic vulnerability of the composite material structure of adobe and timber, we collected and statistically analysed empirical observation samples of 542,214,937 m² and 467,177 buildings that were significantly impacted during the 179 earthquakes that occurred in mainland China from 1976 to 2010. In multi-intensity regions, combined with numerical analysis and a probability model, a non-linear continuous regression model of the vulnerability, considering the empirical seismic damage area (number of buildings) and the ratio of seismic damage, was established. Moreover, a probability matrix model of the empirical seismic damage mean value was provided. Considering the coupling effect of the annual and seismic fortification factors, an empirical seismic vulnerability curve model was constructed in the multiple-intensity regions. A probability matrix model of the mean vulnerability index (MVI) was proposed, and was validated through the above-mentioned reconnaissance sample data. A matrix model of the MVI of the regions (19 provinces in mainland China) based on the parameter (MVI) was established.

• Coupled systems mechanics
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• v.7 no.4
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• pp.395-406
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• 2018

This paper proposes a linear damping model of tire-soil system using semi-empirical method. A test rig was designed and developed to measure the vertical equivalent linear damping ratio of tire only and tire-soil system using Free-Vibration Logarithmic Decay Method. The test was performed with two kinds of tractor tires using a combination of five inflation pressure levels, two soil depths and four soil moisture contents in the paddy soil. The results revealed that the linear damping ratio of tires increased with decreasing tire inflation pressure; the linear damping ratio of tire-soil system also increased with decreasing tire inflation pressure and increased with the increasing soil depth (observed at 80 and 120 mm). It also increased with a relative increase of soil moisture contents (observed at 37.9%, 48.8%, 66.7% and 77.4%). The results also indicated that the damping ratio of tire-soil system was higher than that of tire only. A linear damping model of tire-soil system is proposed as a damping model in parallel which is established based on experimental results and vibration theory. This model will have a great significance in study of tractor vibration.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.291-297
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• 2001

For a stochastic regression model in which the errors are assumed to form a stationary linear process, we show that the difference between the empirical distribution functions of the errors and the estimates of those errors converges uniformly in probability to zero at the rate of $o_{p}$ ( $n^{-}$$\frac{1}{2}$) as the sample size n increases.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.355-368
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• 2023

This article introduces the R package ELCIC (https://cran.r-project.org/web/packages/ELCIC/index.html), which provides an empirical likelihood-based information criterion (ELCIC) for model selection that includes, but is not limited to, variable selection. The empirical likelihood is a semi-parametric approach to draw statistical inference that does not require distribution assumptions for data generation. Therefore, ELCIC is more robust and versatile in the context of model selection compared to the currently existing information criteria. This paper illustrates several applications of ELCIC, including its use in generalized linear models, generalized estimating equations (GEE) for longitudinal data, and weighted GEE (WGEE) for missing longitudinal data under the mechanisms of missing at random and dropout.

• Wind and Structures
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• v.19 no.3
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• pp.233-247
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• 2014

Vortex-induced oscillation is a type of aeroelastic phenomenon, to which extended structures such as long-span bridges are most susceptible. The vortex-induced vibration (VIV) behaviors of a concerned bridge were investigated conventionally in virtue of wind tunnel tests on string-mounted sectional models. This necessitates the building of a linkage between the response of the sectional model and that of the prototype structure. Although many released literatures have related to this issue and provided suggestions, there is a lack of consistency among them. In this study, some theoretical models describing the vortex-induced structural motion, including the linear empirical model, the nonlinear empirical model and the modified (or generalized) nonlinear empirical model, are firstly reviewed. Then, the concept of equivalent mass density is introduced based on the principle that an equal input of energy should result in identical structural amplitudes. Based on these, the theoretical linkages between the amplitude of a section model and that corresponding to the prototype bridge are discussed with different analytical models. Theoretical derivation indicates that such connections are dependent mainly on two factors, one is the presupposed shape of deformation, and the other is the theoretical VIV model employed. The theoretical analysis in this study shows that, in comparison to the nonlinear empirical models, the linear one can result in obvious larger estimations of the full bridges' responses, especially in cases of cable-stayed bridges.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.431-443
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• 2004

For the purpose of disease mapping, we consider the four small area estimation techniques to estimate the mortality rate of small areas; direct, Empirical estimation with total moment estimator and local moment estimator, Estimation based on hierarchial generalized linear model. The estimators are compared by empirical study based on lung cancer mortality data from 2000 Annual Reports on the Cause of Death Statistics in Gyeongsang-Do and Jeonla-Do published by Korean National Statistical Office. Also he stability and efficiency of these estimators are investigated in terms of mean square deviation as well as variation of estimates.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.489-490
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• 2015

We present population synthesis models for the calcium II triplet (CaT), currently the most popular metallicity indicator, based on high-resolution empirical spectral energy distributions (SEDs). Our new CaT models, based on empirical SEDs, show a linear correlation below [Fe/H] ~ -0.5, but the linear relation breaks down in the metal-rich regime by converging to the same equivalent width. This relation shows good agreement with the observed CaT of globular clusters (GCs) in NGC 1407 and the Milky Way. However, a model based on theoretical SEDs does not show this feature of the CaT and fails to reproduce observed GCs in the metal-rich regime. This linear relation may cause inaccurate metallicity determination for metal-rich stellar populations. We have also confirmed that the effect of horizontal-branch stars on the CaT is almost negligible in models based on both empirical and theoretical SEDs. Our new empirical model may explain the difference between the color distributions and CaT distributions of GCs in various early-type galaxies. Based on our model, we claim that the CaT is not a good metallicity indicator for simple stellar populations in the metal-rich regime.

• Proceedings of the KWS Conference
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• 2006.10a
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• pp.271-273
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• 2006

This paper focuses on the developed empirical models for the prediction on top-bead width in GMA(Gas Metal Arc) welding process. Three empirical models have been developed: linear, curvilinear and an intelligent model. Regression analysis was employed fur optimization of the coefficients of linear and curvilinear model, while Genetic Algorithm(GA) was utilized to estimate the coefficients of intelligent model. Not only the fitting of these models were checked, but also the prediction on top-bead width was carried out. ANOVA analysis and contour plots were respectively employed to represent main and interaction effects between process parameters on top-bead width.