• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.301-311
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• 2020

Schwarz's Bayesian information criterion (BIC) is one of the most popular criteria for model selection, that was derived under the assumption of independent and identical distribution. For correlated data in longitudinal studies, Jones (Statistics in Medicine, 30, 3050-3056, 2011) modified the BIC to select the best linear mixed effects model based on the effective sample size where the number of parameters in covariance structure was not considered. In this paper, we propose an extended Jones' modified BIC by considering covariance parameters. We conducted simulation studies under a variety of parameter configurations for linear mixed effects models. Our simulation study indicates that our proposed BIC performs better in model selection than Schwarz's BIC and Jones' modified BIC do in most scenarios. We also illustrate an example of smoking data using a longitudinal cohort of cancer patients.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.225-234
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• 1999

We consider the following semi-parametric non-linear mixed effect regression model : y\ulcorner=f($\chi$\ulcorner;$\beta$)+$\sigma$$\mu$($\chi$\ulcorner)+$\sigma$$\varepsilon$\ulcorner,i=1,…,n,y*=f($\chi$;$\beta$)+$\sigma$$\mu$($\chi$) where y'=(y\ulcorner,…,y\ulcorner) is a vector of n observations, y* is an unobserved new random variable of interest, f($\chi$;$\beta$) represents fixed effect of known functional form containing unknown parameter vector $\beta$\ulcorner=($\beta$$_1$,…,$\beta$\ulcorner), $\mu$($\chi$) is a random function of mean zero and the known covariance function r(.,.), $\varepsilon$'=($\varepsilon$$_1$,…,$\varepsilon$\ulcorner) is the set of uncorrelated measurement errors with zero mean and unit variance and $\sigma$ is an unknown dispersion(scale) parameter. On the basis of finite-sample, small-dispersion asymptotic framework, we derive an absolute lower bound for the asymptotic mean squared errors of prediction(AMSEP) of the regular-consistent non-linear predictors of the new random variable of interest y*. Then we construct an optimal predictor of y* which attains the lower bound irrespective of types of distributions of random effect $\mu$(.) and measurement errors $\varepsilon$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.7A
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• pp.967-977
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• 2000

In this paper, we apply a mixed $H_2/H_{\infty}$ control to a generalized plant of inverted pendulum system represented by an LFR(Linear Fractional Representation). First, in order to obtain the generalized plant, the linear model of the inverted pendulum represented by an LFR(Linear fractional Representation) is derived. In LFR, we consider system uncertainties as three nonlinear components and a pendulum mass uncertainty. Augmenting the LFR model by adding weighting functions, we get a generalized plant. And then, we design a mixed $H_2/H_{\infty}$ controller for the generalized plant. In order to design the mixed $H_2/H_{\infty}$ controller, we use the LMI technique. To evaluate control performances and robust stability of the mixed $H_2/H_{\infty}$ controller designed, we compare it with the $H_{\infty}$ controller through the simulation and experiment. In the result, with the fewer feedback information, the mixed $H_2/H_{\infty}$ controller shows the better control performances and robust stability than the $H_{\infty}$ controller in the sense of pendulum angle.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.69-74
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• 2003

The estimation of pest density is a prime concern of Integrated Pest Management (IPM) because the success of artificial intervention such as spraying pestcides or natural enemies depends on pest density. Also, the spatial pattern of pest population within plants or plots has been studies in various ways. In this study, we applied generalized linear mixed model to Tetranychus urticae Koch , two-spotted spider mite count in glasshouse grown roses. For this analysis, the subject-specific as well as pupulation-averaged approaches are used.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.4
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• pp.53-62
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• 2009

Lee[15] examined quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model where quantity discounts are provided based on the previous order size. During the two periods, the retailer faces stochastic (truncated Poisson distributed) demands and he/she places orders to meet the demands. The manufacturer provides for the retailer a price discount for the second period order if its quantity exceeds the first period order quantity. In this paper we extend the above two-period model to a k-period one (where k < 2) and propose a stochastic nonlinear mixed binary integer program for it. In order to make the program tractable, the nonlinear term involving the sum of truncated Poisson cumulative probability function values over a certain range of demand is approximated by an i-interval piecewise linear function. With the value of i selected and fixed, the piecewise linear function is determined using an evolutionary algorithm where its fitness to the original nonlinear term is maximized. The resulting piecewise linear mixed binary integer program is then transformed to a mixed binary integer linear program. With the k-period model developed, we suggest a solution procedure of receding horizon control style to solve n-period (n < k) order decision problems. We implement Lee's two-period model and the proposed k-period model for the use in receding horizon control style to solve n-period order decision problems, and compare between the two models in terms of the pattern of order quantities and the total profits. Our computational study shows that the proposed model is superior to the two-period model with respect to the total profits, and that order quantities from the proposed model have higher fluctuations over periods.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.295-308
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• 2015

We have experienced a substantial improvement in and cost-drop for genotyping that enables genetic epidemiological studies with large-scale genetic data. Genome-wide association studies have identified more than ten thousand causal variants. Many statistical methods based on linear mixed models have been developed for various goals such as estimating heritability and identifying disease susceptibility locus. Empirical results also repeatedly stress the importance of linear mixed models. Therefore, we review the statistical methods related with to linear mixed models and illustrate the meaning of their estimates.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.562-568
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• 1999

The model using homogenization technique based on energy concept for the prediction of the failure criterion of staple fiber mixed soil was developed to increase the practice and the application of staple fiber as a reinforcement for improving soft ground and agrictural structures. Parameters of the model are aspect ration and volumetric ocntnet of fiber, cohesion and internal friction angle of soil, adhesiion intercept of soil and fiber. It is judged that the model developed in this study is applicable to the soil composed of clay, silt and sand mixed by linear types of fiber such as steel bar, steel fiber , natural fiber etc..

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.361-370
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• 2003

Those who are interested in making inferences concerning linear combination of valiance components in a simple linear regression model with unbalanced nested error structure can use the confidence intervals proposed in this paper. Two approximate confidence intervals for the sum of two variance components in the model are proposed. Simulation study is peformed to compare the methods. The methods are applied to a numerical example and recommendations are given for choosing a proper interval.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.75-78
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• 2003

Those who are interested in making inferences concerning linear combination of variance components in a simple linear regression model with unbalanced nested error structure can use the confidence intervals proposed in this paper. Two approximate confidence intervals for the sum of two variance components in the model are proposed. Simulation study is peformed to compare the methods.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.459-471
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• 2002

In applications using a linear regression model with nested error structure, one might be interested in making inferences concerning variance components. This article proposes approximate confidence intervals on the variance component of the primary level in a simple linear regression model with an unbalanced nested error structure. The intervals are compared using computer simulation and recommendations are provided for selecting an appropriate interval.