• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.397-410
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• 2007

For the two groups data from multivariate binomial distribution, we consider a bootstrap approach to inferring the simultaneous confidence level and its standard error of a collection of the dependent confidence intervals for the difference of proportions with an experimentwise error rate at the a level are presented. The bootstrap method is used to estimate the simultaneous confidence probability for the difference of proportions.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.87-99
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• 1996

We construct bootstrap confidence intervals for reliability, R= P{X>Y}, where X and Y are independent normal random variables. One way ANOVA random effect models are assumed for the populations of X and Y, where standard deviations $\sigma_{x}$ and $\sigma_{y}$ are unequal. We investigate the accuracy of the proposed bootstrap confidence intervals and classical confidence intervals work better than classical confidence interval for small sample and/or large value of R.

• Journal of the Korean Statistical Society
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• v.7 no.2
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• pp.109-119
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• 1978

When a response surface by a seconde order polynomial regression model, the stationary point is obtained by solving simultaneous linear equations. But the point is a function of random variables. We can find a confidence region for this point as Box and Hunter provided. However, the confidence region is often too large to be useful for the experiments, and it is necessary to augment additional design points in order to obtain a satisfactory confidence region for the stationary point. In this note, the author suggests a method how to augment design points "eficiently", and shows the change of the confidence region of the estimated stationary point in a response surface.e surface.

• The Mathematical Education
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• v.55 no.3
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• pp.317-334
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• 2016

Knowledge and data interpretation on statistical estimation was important to have statistical literacy that current curriculum was said not to satisfy. The author investigated mathematics teachers' MKT on statistical estimation concerning interpretation of confidence interval by using questionnaire and interview. SMK of teachers' confidence was limited to the area of textbooks to be difficult to interpret data of real life context. Most of teachers wrongly understood SMK of interpretation of confidence interval to have influence upon PCK making correction of students' wrong concept. SMK of samples and sampling distribution that were basic concept of reliability and confidence interval cognized representation of samples rather exactly not to understand importance and value of not only variability but also size of the sample exactly, and not to cognize appropriateness and needs of each stage from sampling to confidence interval estimation to have great difficulty at proper teaching of statistical estimation. PCK that had teaching method had problem of a lot of misconception. MKT of sample and sampling distribution that interpreted confidence interval had almost no relation with teachers' experience to require opportunity for development of teacher professionalism. Therefore, teachers were asked to estimate statistic and to get confidence interval and to understand concept of the sample and think much of not only relationship of each concept but also validity of estimated values, and to have knowledge enough to interpret data of real life contexts, and to think and discuss students' concepts. So, textbooks should introduce actual concepts at real life context to make use of exact orthography and to let teachers be reeducated for development of professionalism.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.345-351
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• 1997

This paper considers the problem of sequential fixed accuracy confidence set procedure of the aurocorrelations of stationary linear processes. The proposed procedure for fixed-width confidence set is shown to be both asymptotically consistent and asymptotically efficient as the size of the width approaches zero.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.141-150
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• 2006

Penalized likelihood regression for exponential families have been considered by Kim (2005) through smoothing parameter selection and asymptotically efficient low dimensional approximations. We derive approximate Bayesian confidence intervals based on Bayes model associated with lower dimensional approximations to provide interval estimates in penalized likelihood regression and conduct empirical studies to access their properties.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.363-372
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• 2009

The difference of two independent binomial proportions is frequently of interest in biomedical research. The interval estimation may be an important tool for the inferential problem. Many confidence intervals have been proposed. They can be classified into the class of exact confidence intervals or the class of approximate confidence intervals. Ore may prefer exact confidence interval s in that they guarantee the minimum coverage probability greater than the nominal confidence level. However, someone, for example Agresti and Coull (1998) claims that "approximation is better than exact." It seems that when sample size is large, the approximate interval is more preferable to the exact interval. However, the choice is not clear when sample, size is small. In this note, an exact confidence and an approximate confidence interval, which were recommended by Santner et al. (2007) and Lee (2006b), respectively, are compared in terms of the coverage probability and the expected length.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.139-151
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• 1992

Simultaneous confidence intervals for the parameters in the logistic regression models with random regressors are considered. A method based on the bootstrap and its stochastic approximation will be developed. A key idea in using the bootstrap method to construct simultaneous confidence intervals is the concept of prepivoting which uses the transformation of a root by its estimated cumulative distribution function. Repeated use of prepivoting makes the overall coverage probability asymptotically correct and the coverage probabilities of the individual confidence statement asymptotically equal. This method is compared with ordinary asymptotic methods based on Scheffe's and Bonferroni's through Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.997-1005
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• 2003

We can use the logistic model for categorical data when the response variables are binary data. In this paper we consider the problem of constructing the confidence intervals for logistic model in I${\times}$J${\times}$2 contingency table. These constructions are simplified by applying logit transformation. This transforms the problem to consider linear form which called the logit model. After obtaining the confidence intervals for the logit model, the reverse transform is applied to obtain the confidence intervals for the logistic model.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.445-455
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• 2011

Although misclassified binary data occur frequently in practice, the statistical methodology available for the data is rather limited. In particular, the interval estimation of population proportion has relied on the classical Wald method. Recently, Lee and Choi (2009) developed a new confidence interval by applying the Agresti-Coull's approach and showed the efficiency of their proposed confidence interval numerically, but a theoretical justification has not been explored yet. Therefore, a Bayesian model for the misclassified binary data is developed to consider the Agresti-Coull confidence interval from a theoretical point of view. It is shown that the Agresti-Coull confidence interval is essentially a Bayesian confidence interval.