• 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.27 no.4
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• pp.553-560
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• 2014

This paper deals with estimable functions of parameters of less than full rank linear model. In general, the parameters of an overspecified model are not uniquely determined by least squares solutions. It discusses how to formulate linear estimable functions as functions of parameters in the model and shows how to use projection matrices to check out whether a parameter or function of the pamameters is estimable. It also presents a method to form a basis set of estimable functions using linearly independent characteristic vectors generating the row space of the model matrix.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.523-534
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• 2010

The purpose of this paper is to forecast the numbers of students in a capital areas until 2027 year by using the moving average methods for estimating the number of student at the elementary, meddle and high-school. It is analyzed the third student number at the high schools and the entrance quota of colleges and universities around capital areas until 2027. The result of this paper is that there are no problems to keep the current entrance quota of colleges and universities around capital areas until 2027.

• Communications for Statistical Applications and Methods
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• v.28 no.4
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• pp.393-410
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• 2021

The Korean Long-Term Care Insurance (K-LTCI) provides financial support for long-term care service to people who need various types of assistance with daily activities. As the number of elderly people in Korea is expected to increase in the future, the demand for long-term care insurance would also increase over time. Projection of future expenditure on K-LTCI depends on the number of beneficiaries within the grading system of K-LTCI based on the test scores of applicants. This study investigated the suitability of mixture distributions to the model K-LTCI score distribution using recent empirical data on K-LTCI, provided by the National Health Insurance Service (NHIS). Based on the developed mixture models, the number of beneficiaries in each grade and its variability under the current grading system were estimated by simulation. It was observed that a mixture model is suitable for K-LTCI score distribution and may prove useful in devising a funding plan for K-LTCI benefit payment and investigating the effects of any possible revision in the K-LTCI grading system.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.495-504
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• 2012

In this study, we propose a statistical model based on projection that generates interview scores. In this model, each interviewee's true score and its related variable are viewed as X, Y values respectively in the two dimensional plane, and each interviewer's score is the projected score of true score X to the axis rotated by some angle, which reflects the interviewer's perspective. Each interviewer's observed interview score is obtained by adding personal bias and observed error to this projected score. We compared commonly used standardizing methods of interview scores such as trimmed mean method, rank method, and z-score method based on the proposed statistical model. In this simulation, two types of interview methods, two numbers of interviewers, two degrees of interviewers' expertise and two distributions and three correlations between actual score and its related variable are all considered.

• Journal of Korea Water Resources Association
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• v.51 no.spc
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• pp.1067-1078
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• 2018

Water resources projection typically consists of several stages including emission scenarios, global circulation models (GCMs), downscaling techniques, and hydrological models, and each stage is a source of total uncertainty in water resources projection. Several studies proposed methods to quantify the relative contribution of each stage to total uncertainty, and we call such analysis uncertainty decomposition. Uncertainty decomposition enables us to investigate the stages yielding large uncertainties and to establish the uncertainty reduction plan that reflects them. Interactions between stages is one of the important issues to be considered in uncertainty decomposition. This study suggests a new uncertainty decomposition method considering interaction effect. The proposed method has an advantage of decomposing the total uncertainty to the uncertainty from each stage considering both the main and interactions effects. We apply the proposed method to streamflow projection for Chungju Dam basin. The results show that the uncertainties from the main effects are larger than the uncertainties from interaction effects in both summer and winter. Using the proposed uncertainty decomposition method, we show that the GCM stage is the largest source of the total uncertainty in summer and the downscaling technique stage is the one in winter among the following four stages: emission scenarios, GCMs, downscaling techniques, and hydrological models.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.1-11
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• 2010

This study aims to improve the more confident and efficient projection method that is to estimate the Number of Household per Family scales(NHF) in projecting the Household Heath care Expenditure(HHE). For this purpose, this paper suggested three results of the research. First, because projecting the NHF does not reflect the recent socio-demographic trends in the process of projecting the National Health Expenditure(NHE),the prior projection results have serious problem in the confidence and political availability. Second, the projection results about the HHE might be underestimated relative to the real one. Third, in order to estimate the more confident and efficient estimates of the HHE, the estimated NHF reflecting the socio-demographic trend must be used to project the one. There is an alternative method that the NHF and the increasing or decreasing rate of them which are regularly surveyed and suggested by the KOSIS should be used to project the process.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.799-805
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• 2014

This paper deals with a method for getting the Type III sums of squares on the basis of projections under the assumption of two-way fixed effects model. For unbalanced data in general total sum of squares is not equal to the sum of componentwise Type III sums of squares. There are some differencies between two quantities. The suggested method using projections can detect where the differences occur and how much they are different. The traditional ANOVA method could not explain clearly the differences. It also discusses how eigenvectors and eigenvalues of the projection matrices can be used to get the Type III sums of squares.

• 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.

• Journal of Korean Society for Quality Management
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• v.24 no.3
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• pp.94-110
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• 1996

Two regression models for explaining the tire performances (especially conering coefficients) by tire design and experimental factors are built. One is the ordinary regression model, and the explaining variables in the model are selected by a stepwise method. The other model is built by a modern nonparametric regression technique, called projection pursuit regression. Then two models are compared and combined, so that the relationship between the tire performances and design factors are well figured out. The optimal experimental design issue and future research ideas are also discussed.