• Communications for Statistical Applications and Methods
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• 제9권2호
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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.

• 산업경영시스템학회지
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• 제20권41호
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• pp.213-220
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• 1997

Process capability Indices compare the actual performance of manufacturing process to the desired performance. The relationship between the capability index Cpm and the expected squared error loss provides an intuitive interpretation of Cpm. By putting the loss in relative terms a user needs only to specify the target and the distance from the target at which the product would have zero worth, or alternatively, the loss at the specification limits. Confidence limits for the expected relative loss are discussed, and numerical illustration is given.

• Communications for Statistical Applications and Methods
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• 제6권2호
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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.

• Journal of the Korean Statistical Society
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• 제35권3호
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• pp.317-329
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• 2006

In the problem of estimating the error variance in the balanced fixed- effects one-way analysis of variance (ANOVA) model, Ghosh (1994) proposed hierarchical Bayes estimators and raised a conjecture for which all of his hierarchical Bayes estimators are admissible. In this paper we prove this conjecture is true by representing one-way ANOVA model to the distributional form of a multiparameter exponential family.

• Journal of the Korean Statistical Society
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• 제35권1호
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• pp.63-77
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• 2006

Maximum product of spacings estimator is proposed in this paper as a competent alternative of maximum likelihood estimator for the parameters of exponentiated-Weibull distribution, which does work even when the maximum likelihood estimator does not exist. In addition, a Bayes type estimator known as generalized maximum likelihood estimator is also obtained for both of the shape parameters of the aforesaid distribution. Though, the closed form solutions for these proposed estimators do not exist yet these can be obtained by simple appropriate numerical techniques. The relative performances of estimators are compared on the basis of their relative risk efficiencies obtained under symmetric and asymmetric losses. An example based on simulated data is considered for illustration.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.887-894
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• 2009

The two-stage minimum risk point estimation of mean, the probability of success in a sequence of Bernoulli trials, is considered for the case where loss is taken to be symmetrized relative squared error of estimation, plus a fixed cost per observation. First order asymptotic expansions are obtained for large sample properties of two-stage procedure. Monte Carlo simulation is carried out to obtain the expected sample size that minimizes the risk and to examine its finite sample behavior.

• Korean Chemical Engineering Research
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• 제61권3호
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• pp.388-393
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• 2023

지도 학습 기반의 신경 망을 활용한 공학적 자료의 분석은 화학공학 공정 최적화, 미세 먼지 농도 추정, 열역학적 상평형 예측, 이동 현상 계의 물성 예측 등 다양한 분야에서 활용되고 있다. 신경 망의 지도 학습은 학습 자료를 요구하며, 주어진 학습 자료의 구성에 따라 학습 성능이 영향을 받는다. 빈번히 관찰되는 공학적 자료 중에는 DNA의 길이, 분석 물질의 농도 등과 같이 로그 간격으로 주어지는 자료들이 존재한다. 본 연구에서는 넓은 범위에 분포된 로그 간격의 학습 자료를 기계 학습으로 처리하는 경우, 사용 가능한 손실 함수들의 학습 성능을 정량적으로 평가하였으며, 적합한 학습 자료 구성 방식을 연구하였다. 이를 수행하고자, 100×100의 가상 이미지를 활용하여 기계 학습의 회귀 과업을 구성하였다. 4개의 손실 함수들에 대하여 (i) 오차 행렬, (ii) 최대 상대 오차, (iii) 평균 상대 오차로 정량적 평가하여, mape 혹은 msle가 본 연구에서 다룬 과업에 대해 최적의 손실 함수가 됨을 알아내었다. 또한, 학습 자료의 값이 넓은 범위에 걸쳐 분포하는 경우, 학습 자료의 구성을 로그 간격 등을 고려하여 균등 선별하는 방식이 높은 학습 성능을 보임을 밝혀내었다. 본 연구에서 다룬 회귀 과업은 DNA의 길이 예측, 생체 유래 분자 분석, 콜로이드 용액의 농도 추정 등의 공학적 과업에 적용 가능하며, 본 결과를 활용하여 기계 학습의 성능과 학습 효율의 증대를 기대할 수 있을 것이다.