• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.349-359
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• 2015

We study a semiparametric Bayesian approach to small area estimation under a nested error linear regression model with area level covariate subject to measurement error. Consideration is given to radial basis functions for the regression spline and knots on a grid of equally spaced sample quantiles of covariate with measurement errors in the nested error linear regression model setup. We conduct a hierarchical Bayesian structural measurement error model for small areas and prove the propriety of the joint posterior based on a given hierarchical Bayesian framework since some priors are defined non-informative improper priors that uses Markov Chain Monte Carlo methods to fit it. Our methodology is illustrated using numerical examples to compare possible models based on model adequacy criteria; in addition, analysis is conducted based on real data.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.187-192
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• 2005

For the problem of variable selection in linear models, we consider the errors are correlated with V covariance matrix. Hocking's theorems on the effects of the overfitting and the undefitting in linear model are extended to the less than full rank and correlated error model, and to the ANCOVA model

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.325-336
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• 1999

Collinearity among independent variables can have severe effects on the precision of response estimation for some region of interest in the experiments with mixture. A method of finding optimal linear restriction on regression parameter in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.366-370
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• 2003

This paper is on weighted model reduction using structurally balanced truncation. For a given weighted(single or double-sided) transfer function, a state space realization with the linear fractional transformation form is obtained. Then we prove that two block diagonal LMI(linear matrix inequality) solutions always exist, and it is possible to get a reduced order model with guaranteed stability and a priori error bound. Finally, two examples are used to show the validity of proposed weighted reduction method, and the method is compared with other existing methods.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.189-199
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• 2020

This paper studies a Bayesian ordered multiple linear regression model with skew normal error. It is reasonable that the kind of inherent information available in an applied regression requires some constraints on the coefficients to be estimated. In addition, the assumption of normality of the errors is sometimes not appropriate in the real data. Therefore, to explain such situations more flexibly, we use the skew-normal distribution given by Sahu et al. (The Canadian Journal of Statistics, 31, 129-150, 2003) for error-terms including normal distribution. For Bayesian methodology, the Markov chain Monte Carlo method is employed to resolve complicated integration problems. Also, under the improper priors, the propriety of the associated posterior density is shown. Our Bayesian proposed model is applied to NZAPB's apple data. For model comparison between the skew normal error model and the normal error model, we use the Bayes factor and deviance information criterion given by Spiegelhalter et al. (Journal of the Royal Statistical Society Series B (Statistical Methodology), 64, 583-639, 2002). We also consider the problem of detecting an influential point concerning skewness using Bayes factors. Finally, concluding remarks are discussed.

• Journal of Information Technology Applications and Management
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• v.28 no.4
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• pp.13-20
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• 2021

In this paper, I was applied the life distribution following linear failure rate distribution, Lindley distribution and Burr-Hatke exponential distribution extensively used in the arena of software reliability and were associated the reliability possessions of the software using the nonhomogeneous Poisson process with finite failure. Furthermore, the average value functions of the life distribution are non-increasing form. Case of the linear failure rate distribution (exponential distribution) than other models, the smaller the estimated value estimation error in comparison with the true value. In terms of accuracy, since Burr-Hatke exponential distribution and exponential distribution model in the linear failure rate distribution have small mean square error values, Burr-Hatke exponential distribution and exponential distribution models were stared as the well-organized model. Also, the linear failure rate distribution (exponential distribution) and Burr-Hatke exponential distribution model, which can be viewed as an effectual model in terms of goodness-of-fit because the larger assessed value of the coefficient of determination than other models. Through this study, software workers can use the design of mean square error, mean value function as a elementary recommendation for discovering software failures.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.171-179
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• 2006

For the problem of variable selection in linear models, we consider the errors are correlated with V covariance matrix. Hocking's theorems on the effects of the overfitting and the underfitting in linear model are extended to the less than full rank and correlated error model, and to the ANCOVA model.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.85-92
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• 2003

We consider the partially linear model E(Y) : X$^{t}$ $\beta$＋η(Z) when the X's are measured with additive error. The semiparametric likelihood estimation ignoring the measurement error gives inconsistent estimator for both $\beta$ and η(.). In this paper we suggest the SIMEX estimator for f to correct the bias induced by measurement error, and explore its properties. We show that the rational linear extrapolant is proper in extrapolation step in the sense that the SIMEX method under this extrapolant gives consistent estimator It is also shown that the SIMEX estimator is asymptotically equivalent to the semiparametric version of the usual parametric correction for attenuation suggested by Liang et al. (1999) A simulation study is given to compare two variance estimating methods for SIMEX estimator.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.3 s.96
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• pp.215-221
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• 1999

The object of the thermal error compensation system in machine tools is improving the accuracy of a machine tool through real time error compensation. The accuracy of the machine tool totally depends on the accuracy of thermal error model. A thermal error model can be obtained by appropriate combination of temperature variables. The proposed method for optimal variable selection in the thermal error model is based on correlation grouping and successive regression analysis. Collinearity matter is improved with the correlation grouping and the judgment function which minimizes residual mean square is used. The linear model is more robust against measurement noises than an engineering judgement model that includes the higher order terms of variables. The proposed method is more effective for the applications in real time error compensation because of the reduction in computational time, sufficient model accuracy, and the robustness.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.153-161
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• 2009

We consider a logistic model with random effects as the superpopulation for estimating the small area pro-portions. The best linear unbiased predictor under linear mired model is popular in small area estimation. We use this type of estimator under logistic mixed motel for the small area proportions, on which the estimation of mean squared error is also discussed. Two kinds of estimation methods, the parametric bootstrap and the linear approximation will be compared through a Monte Carlo study in the respects of the normality assumption on the random effects distribution and also the magnitude of sample sizes on the approximation.