• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.31-39
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• 2015

This paper deals with a method for estimating variance components on the basis of projections under the assumption of random effects model. It discusses how to use projections for getting sums of squares to estimate variance components. The use of projections makes the vector subspace generated by the model matrix to be decomposed into subspaces that are orthogonal each other. To partition the vector space by the model matrix stepwise procedure is used. It is shown that the suggested method is useful for obtaining Type I sum of squares requisite for the ANOVA method.

• Korean Management Science Review
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• v.8 no.1
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• pp.127-133
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• 1991

본 연구에서는 Karmarkar법의 변형인 Todd&Burrell 알고리즘을 분석하고 이 알고리즘의 수행속도를 증가시키기 위한 몇가지 방안을 제시하였다. 또한, 몇가지 실험을 통하여 제안된 방안들을 비교 분석하였다. 사영행렬의 계산에 QR 분해법과 Cholesky 분해법을 도입함으로써 계산 시간을 줄일 수 있었고, 구내최적화를 위한 개선폭의 결정에 비율검정법과 선형탐색법을 사용함으로써 수행횟수 및 총 수행시간을 줄일 수 있었다. 수행실험을 통하여 알고리즘을 분석한 결과, 수행시간의 대부분을 사영행렬의 계산이 차지하는 것으로 나타나 이론적으로 계산복잡도를 분석한 결과와 일치하였다. 또한, 사영행렬과 개선폭의 결정에 사용된 각 방법들을 실험을 통해 비교 분석한 바로는 사영행렬의 계산에 있어서 Cholesky 분해법이 Gauss소거법이나 QR 분해법을 쓰는 경우보다 우수했으며, 개선폭을 결정하는 데 있어서는 비율검정법이 속도면에서 가장 우수했다.

• Journal of the Korean Data and Information Science Society
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• v.24 no.2
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• pp.333-339
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• 2013

This paper discusses a method for getting a basis set of estimable functions of less than full rank linear model. Since model parameters are not estimable estimable functions should be identified for making inferences proper about them. So, it suggests a method of using full rank factorization of model matrix to find estimable functions in easy way. Although they might be obtained in many different ways of using model matrix, the suggested full rank factorization technique could be one of much easier methods. It also discusses how to use projection matrix to identify estimable functions.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.487-494
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• 2012

This paper discusses a method for getting a basis set of estimable functions of model parameters in a two-way fixed effects model. Since the fixed effects model has more parameters than those that can be estimated, model parameters are not estimable. So it is not possible to make inferences for nonestimable functions of parameters. When the assumed model of matrix notation is reparameterized by the estimable functions in a basis set, it also discusses how to use projections for the estimation of estimable functions.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1155-1163
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• 2016

This paper deals with an estimation procedure of variance components in a mixed effects model by projections. Projections are used to obtain sums of squares instead of using reductions in sums of squares due to fitting both the assumed model and sub-models in the fitting constants method. A projection matrix can be obtained for the residual model at each step by a stepwise procedure to test the hypotheses. A weighted least squares method is used for the estimation of fixed effects. Satterthwaite's approximation is done for the confidence intervals for variance components.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.373-381
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• 2011

This paper discusses how to get the sums of squares due to treatment factors when Type I Analysis is used by projections for the analysis of data under the assumption of a two-way ANOVA model. The suggested method does not need to calculate the residual sums of squares for the calculation of sums of squares. There-fore, the calculation is easier and faster than classical ANOVA methods. It also discusses how eigenvectors and eigenvalues of the projection matrices can be used to get the calculation of sums of squares. An example is given to illustrate the calculation procedure by projections for unbalanced data.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.347-354
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• 2015

This paper deals with a method for intrablock anlaysis of balanced incomplete block designs on the basis of projections under the assumption of mixed effects model. It shows how to construct a model at each step by the stepwise procedure and discusses how to use projection for the analysis of intrablock. Projections are obtained in vector subspaces orthogonal to each other. So the estimates of the treatment effects are not affected by the block effects. The estimability of a parameter or a function of parameters is discussed and eigenvectors are dealt for the construction of estimable functions.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1093-1101
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• 2015

This paper discusses nested design models when nesting occurs in treatment structure and design structure. Some are fixed and others are random; subsequently, the fixed factors having a nested design structure are assumed to be nested in the random factors. The treatment structure can involve random and fixed effects as well as a design structure that can involve several sizes of experimental units. This shows how to use projections for sums of squares by fitting the model in a stepwise procedure. Expectations of sums of squares are obtained via synthesis. Variance components of the nested design model are estimated by the method of moments.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2002.11a
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• pp.226-230
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• 2002

This paper proposes a method of improvement of accuracy of projective transformation matrix for Image Mosaicing. Using shift theorem, we extracted global translation components between images and using translation components, we found matching points between images so we solve general matching point problem we extracted highly trusted matching point using RANSAC algorithm. we normalized matching point coordinates and improved accuracy of projective transformation matrix.