• Title/Summary/Keyword: error sum of squares

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Hierarchical Bayes Estimators of the Error Variance in Balanced Fixed-Effects Two-Way ANOVA Models

  • Kim, Byung-Hwee;Dong, Kyung-Hwa
    • Communications for Statistical Applications and Methods
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    • v.6 no.2
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    • pp.487-500
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    • 1999
  • We propose a class of hierarchical Bayes estimators of the error variance under the relative squared error loss in balanced fixed-effects two-way analysis of variance models. Also we provide analytic expressions for the risk improvement of the hierarchical Bayes estimators over multiples of the error sum of squares. Using these expressions we identify a subclass of the hierarchical Bayes estimators each member of which dominates the best multiple of the error sum of squares which is known to be minimax. Numerical values of the percentage risk improvement are given in some special cases.

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Numerical Investigations in Choosing the Number of Principal Components in Principal Component Regression - CASE I

  • Shin, Jae-Kyoung;Moon, Sung-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.8 no.2
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    • pp.127-134
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    • 1997
  • A method is proposed for the choice of the number of principal components in principal component regression based on the predicted error sum of squares. To do this, we approximately evaluate that statistic using a linear approximation based on the perturbation expansion. In this paper, we apply the proposed method to various data sets and discuss some properties in choosing the number of principal components in principal component regression.

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Derivation of error sum of squares of two stage nested designs and its application (이단계 지분계획법의 오차제곱합 유도와 그 활용)

  • Kim, Daehak
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1439-1448
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    • 2013
  • The analysis of variance for randomized block design or two way classification data is well known. In this paper, particularly, we considered two stage nested design in which the levels of one factor is not identical for different levels of another factor. We investigate the structural properties of two stage nested design and the properties of error sum of squares for random effect model. For the application of two way nested design, we consider two-period crossover design which is used commonly for the equivalence test to bio-similar product. The confidence interval estimation of the difference of two population means in the crossover design is discussed based on statistical package SPSS.

Weighted Least Absolute Error Estimation of Regression Parameters

  • Song, Moon-Sup
    • Journal of the Korean Statistical Society
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    • v.8 no.1
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    • pp.23-36
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    • 1979
  • In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

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Hierarchical Bayes Estimators of the Error Variance in Two-Way ANOVA Models

  • Chang, In Hong;Kim, Byung Hwee
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.315-324
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    • 2002
  • For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.

ANALYSIS OF FIRST-ORDER SYSTEM LEAST-SQUARES FOR THE OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS

  • Choi, Young-Mi;Kim, Sang-Dong;Lee, Hyung-Chun;Shin, Byeong-Chun
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.55-68
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    • 2007
  • First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

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ANALYSIS AND COMPUTATIONS OF LEAST-SQUARES METHOD FOR OPTIMAL CONTROL PROBLEMS FOR THE STOKES EQUATIONS

  • Choi, Young-Mi;Kim, Sang-Dong;Lee, Hyung-Chun
    • Journal of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.1007-1025
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    • 2009
  • First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

The NHPP Bayesian Software Reliability Model Using Latent Variables (잠재변수를 이용한 NHPP 베이지안 소프트웨어 신뢰성 모형에 관한 연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul
    • Convergence Security Journal
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    • v.6 no.3
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    • pp.117-126
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    • 2006
  • Bayesian inference and model selection method for software reliability growth models are studied. Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. In this paper, could avoid multiple integration using Gibbs sampling, which is a kind of Markov Chain Monte Carlo method to compute the posterior distribution. Bayesian inference for general order statistics models in software reliability with diffuse prior information and model selection method are studied. For model determination and selection, explored goodness of fit (the error sum of squares), trend tests. The methodology developed in this paper is exemplified with a software reliability random data set introduced by of Weibull distribution(shape 2 & scale 5) of Minitab (version 14) statistical package.

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A Nonlinear Observer Design for Estimating State-of-Charge of Lithium Polymer Battery (리튬폴리머 배터리 잔존충전용량 추정을 위한 비선형 관측기 설계)

  • Yoo, Seog-Hwan
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.3
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    • pp.300-304
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    • 2012
  • This paper presents a nonlinear observer design method for SOC(state-of-charge) estimation of Lithium polymer battery cell. The dynamic equation of the battery cell is modeled as a simple RC electrical circuit with a nonlinear voltage source and the parameters are obtained via nonlinear optimization. Using the sum of squares decomposition, the observer gain is designed such that the error dynamics is asymptotically stable and the decay rate is below the prescribed value. In order to illustrate the performance of the observer, a computer simulation is performed using the experimental data with the UDDS(urban dynamometer driving schedule) current profile.

Numerical Investigations in Choosing the Number of Principal Components in Principal Component Regression - CASE II

  • Shin, Jae-Kyoung;Moon, Sung-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.163-172
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    • 1999
  • We propose a cross-validatory method for the choice of the number of principal components in principal component regression based on the magnitudes of correlations with y. There are two different manners in choosing principal components, one is the order of eigenvalues(Shin and Moon, 1997) and the other is that of correlations with y. We apply our method to various data sets and compare results of those two methods.

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