• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.205-213
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• 2007

In this paper, the normal mixture model subjected to general linear restriction for component-means based on linear regression is proposed, and its fitting method by EM algorithm and Lagrange multiplier is provided. This model is applied to gene clustering of microarray expression data, which demonstrates it has very good performances for real data set. This model also allows to obtain the clusters that an analyst wants to find out in the fashion that the hypothesis for component-means is represented by the design matrices and the linear restriction matrices.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 추계 학술발표회 논문집
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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

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
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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.

• 한국운동역학회지
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• 제27권1호
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• pp.67-74
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• 2017

Objective: The purpose of this study was to apply a general linear model in statistics to marker position vectors used to study human joint rotational motion in biomechanics. Method: For this purpose, a linear model that represents the effect of the center of hip joint rotation and the rotation of the marker position on the response was formulated. Five male subjects performed hip joint functional motions, and the positions of nine markers attached on the thigh with respect to the pelvic coordinate system were acquired at the same time. With the nine marker positions, the center of hip joint rotation and marker positions on the thigh were estimated as parameters in the general linear model. Results: After examining the fitted model, this model did not fit the data appropriately. Conclusion: A refined model is required to take into account specific characteristics of longitudinal data and other covariates such as soft tissue artefacts.

• 응용통계연구
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• 제28권2호
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• pp.361-369
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• 2015

연속측도의 반응변수가 반복측정된 실험 자료의 분석을 위해 흔히 선형혼합모형이 사용된다. 그러나, 잔차의 분포가 이분산성이거나 비정규성을 가질 때 표준적인 선형혼합모형은 적절하지 않은 결과를 가져온다. 잔차의 분포가 두터운 꼬리를 가진 비정규분포를 보이는 타이어 필드시험 데이터를 로버스트 선형혼합모형에 적합시킴으로써 보다 더 정확하고 신뢰할 수 있는 분석결과를 얻을 수 있다. 추가적으로 신뢰성 분석 결과를 제시한다.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• 한국운동역학회지
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• 제28권2호
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• pp.127-134
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• 2018

Objective: In a statistical linear model estimating the center of rotation of a human hip joint, which is the parameter related to the mean of response vectors, assumptions of homoscedasticity and independence of position vectors measured repeatedly over time in the model result in an inefficient parameter. We, therefore, should take into account the variance-covariance structure of longitudinal responses. The purpose of this study was to estimate the efficient center of rotation vector of the hip joint by using covariance pattern models. Method: The covariance pattern models are used to model various kinds of covariance matrices of error vectors to take into account longitudinal data. The data acquired from functional motions to estimate hip joint center were applied to the models. Results: The results showed that the data were better fitted using various covariance pattern models than the general linear model assuming homoscedasticity and independence. Conclusion: The estimated joint centers of the covariance pattern models showed slight differences from those of the general linear model. The estimated standard errors of the joint center for covariance pattern models showed a large difference with those of the general linear model.

• Journal of the Korean Statistical Society
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• 제8권2호
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• pp.107-109
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• 1979

Consider a linear model with n observations and k explanatory variables: (1)b $y=X\beta+u, u\simN(0,\sigma^2I_n)$. We assume that the model satisfies the ideal conditions. Consider the general linear constraints on regression coefficient vector: (2) $R\beta=r$, where R and r are known matrices of orders $q\timesk$ and q\times1$ respectively, and the rank of R is $qk+q$.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.1007-1015
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• 2003

In this paper we introduced a new score generating function for the rank dispersion function in a general linear model. Based on the new score function, we derived the null asymptotic theory of the rank-based hypothesis testing in a linear model. In essence we showed that several rank test statistics, which are primarily focused on our new score generating function and new dispersion function, are mainly distribution free and asymptotically converges to a chi-square distribution.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.807-815
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• 2002

We consider a more general linear regression super-population model than the one of Chaudhuri and Stronger(1992) . We can find the same type of the best linear unbiased(BLU) predictor as that of Chaudhuri and Stenger and see that the optimal design is again a purposive one which prescribes choosing one of the samples of size n which has $\chi$ closest to $\bar{X}$.