• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.129-140
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• 2009

In this paper, we consider simultaneous confidence intervals for the difference of proportions between two groups taken from multivariate binomial distributions in a nonparametric way. We briefly discuss the construction of simultaneous confidence intervals using the method of adjusting the p-values in multiple tests. The features of bootstrap simultaneous confidence intervals using non-pooled samples are presented. We also compute confidence intervals from the adjusted p-values of multiple tests in the Westfall (1985) style based on a pooled sample. The average coverage probabilities of the bootstrap simultaneous confidence intervals are compared with those of the Bonferroni simultaneous confidence intervals and the Sidak simultaneous confidence intervals. Finally, we give an example that shows how the proposed bootstrap simultaneous confidence intervals can be utilized through data analysis.

• Physical Therapy Korea
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• v.23 no.2
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• pp.93-99
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• 2016

Background: Parametric statistical procedures are typically conducted under the condition in which a sample distribution is statistically identical with its population. In reality, investigators use inferential statistics to estimate parameters based on the sample drawn because population distributions are unknown. The uncertainty of limited data from the sample such as lack of sample size may be a challenge in most rehabilitation studies. Objects: The purpose of this study is to review the bootstrapping method to overcome shortcomings of limited sample size in rehabilitation studies. Methods: Articles were reviewed. Results: Bootstrapping method is a statistical procedure that permits the iterative re-sampling with replacement from a sample when the population distribution is unknown. This statistical procedure is to enhance the representativeness of the population being studied and to determine estimates of the parameters when sample size are too limited to generalize the study outcome to target population. The bootstrapping method would overcome limitations such as type II error resulting from small sample sizes. An application on a typical data of a study represented how to deal with challenges of estimating a parameter from small sample size and enhance the uncertainty with optimal confidence intervals and levels. Conclusion: Bootstrapping method may be an effective statistical procedure reducing the standard error of population parameters under the condition requiring both acceptable confidence intervals and confidence level (i.e., p=.05).

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.115-127
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• 2009

The purpose of statistical analyses of array-CGH experiment data is to divide the whole genome into regions of equal copy number, to quantify the copy number in each region and finally to evaluate its significance of being different from two. Several statistical procedures have been proposed which include the circular binary segmentation, and a Gaussian based local regression for detecting break points (GLAD) by estimating a piecewise constant function. We propose in this note a penalized spline regression and its simultaneous confidence band(SCB) approach to evaluate the statistical significance of regions of genetic gain/loss. The region of which the simultaneous confidence band stays above 0 or below 0 can be considered as a region of genetic gain or loss. We compare the performance of the SCB procedure with GLAD and hidden Markov model approaches through a simulation study in which the data were generated from AR(1) and AR(2) models to reflect spatial dependence of the array-CGH data in addition to the independence model. We found that the SCB method is more sensitive in detecting the low level copy number alterations.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.625-632
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• 2004

We consider the empirical Bayes confidence intervals that attain a specified level of EB coverage for the scale parameter in the Burr distribution under type II censoring data. Also, we compare the coverage probabilities and the expected confidence interval lengths for these confidence intervals through simulation study.

• Journal of the Korean Statistical Society
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• v.20 no.1
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• pp.44-56
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• 1991

For all pairwise comparisons of treatments, Bayesian simultaneous confidence intervals are proposed and studied. First Bayesian solutions are obtained for a fixed prior, and then prior parameters are estimated by a parametric empirical Bayesian method. The nominal confidence level is shown to be controlled asymptotically. An extension to the unbalanced design is also considered.

• Journal of the Korean Statistical Society
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• v.15 no.2
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• pp.107-117
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• 1986

This paper gives some new results on the multivariate linear calibration problem in the case when the controlled variable is univariate. Firstly, a condition under which one can obtain a finite closed confidence interval of $x_0$(unknown controlled variable) is suggested. Secondly, this article considers a criterion to find out whether the multivariate calibration significantly shortens the confidence interval of $x_0$ and supports this criterion by examples. Finally, a multivariate extension of the results in Lwin Maritz (1982) is given.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.108-117
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• 1991

A parametric empirical Bayes procedure is proposed and studied to compare treatments simultaneously with the best. Minimum Bayes risk lower bounds are derived for an additive loss function, and their relationship with Bayesian simultaneous confidence lower bounds is given. For the proposed empirical Bayes procedure, the nominal confidence level both in Bayesian sense and in frequentist's sense is shown to be controlled asymptotically. For practical implementation, a measure of significance similar to f-value is suggested with an illustrative example.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.643-653
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• 2008

Application of the bootstrap to problems in multistage inference procedures are discussed in normal and other related models. After a general introduction to these procedures, here we explore in multistage fixed precision inference in models. We present numerical comparisons of these procedures based on bootstrap critical points for small and moderate sample sizes obtained via extensive sets of simulated experiments. It is expected that the procedure based on bootstrap leads to better results.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.361-370
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• 2003

Those who are interested in making inferences concerning linear combination of valiance components in a simple linear regression model with unbalanced nested error structure can use the confidence intervals proposed in this paper. Two approximate confidence intervals for the sum of two variance components in the model are proposed. Simulation study is peformed to compare the methods. The methods are applied to a numerical example and recommendations are given for choosing a proper interval.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.359-370
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• 1999

We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.