• 응용통계연구
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• 제22권1호
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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.

• Journal of the Korean Statistical Society
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• 제21권2호
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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.

• Journal of the Korean Statistical Society
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• 제36권3호
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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.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.53-62
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• 1994

When a comparison is made with respect to the unknown best treatment, Hsu (1984, 1985) proposed the so called multiple comparisons procedures with the best in the analysis of variance model. Applying Hsu's results to the analysis of covariance model, simultaneous confidence intervals for multiple comparisons with the best in a balanced one-way layout with a random covariate are developed and are applied to a real data example.

• Journal of the Korean Statistical Society
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• 제20권1호
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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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• 제32권3호
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• pp.299-309
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• 2003

Let ${\pi}_1,...,{\pi}_{k}$k($\geq$2) independent logistic populations such that the cumulative distribution function (cdf) of an observation from the population ${\pi}_{i}$ is $$F_{i}\;=\; {\frac{1}{1+exp{-\pi(x-{\mu}_{i})/(\sigma\sqrt{3})}}},\;$\mid$x$\mid$<\;{\infty}$$ where ${\mu}_{i}(-{\infty}\; < \; {\mu}_{i}\; <\; {\infty}$ is unknown location mean and ${\delta}^2$ is known variance, i ＝ 1,..., $textsc{k}$. Let ${\mu}_{[k]}$ be the largest of all ${\mu}$'s and the population ${\pi}_{i}$ is defined to be 'good' if ${\mu}_{i}\;{\geq}\;{\mu}_{[k]}\;-\;{\delta}_1$, where ${\delta}_1\;>\;0$, i = 1,...,$textsc{k}$. A selection procedure based on sample median is proposed to select a subset of $textsc{k}$ logistic populations which includes all the good populations with probability at least $P^{*}$(a preassigned value). Simultaneous confidence intervals for the differences of location parameters, which can be derived with the help of proposed procedures, are discussed. If a population with location parameter ${\mu}_{i}\;<\;{\mu}_{[k]}\;-\;{\delta}_2({\delta}_2\;>{\delta}_1)$, i ＝ 1,...,$textsc{k}$ is considered 'bad', a selection procedure is proposed so that the probability of either selecting a bad population or omitting a good population is at most 1­ $P^{*}$.

• International Journal of Reliability and Applications
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• 제3권1호
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• pp.37-50
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• 2002

Simultaneous estimation of accuracy and probability corresponding to a prediction interval is considered in this study. Traditional application of confidence interval forecasting consists in evaluation of interval limits for a given significance level. The wider is this interval, the higher is probability and the lower is the forecast precision. In this paper a measure of stochastic forecast accuracy is introduced, and a procedure for balanced estimation of both the predicting accuracy and confidence probability is elaborated. Solution can be obtained in an optimizing approach. Suggested method is applied to constructing confidence intervals for parameters estimated by normal and t distributions

• 한국시뮬레이션학회논문지
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• 제3권1호
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• pp.17-28
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• 1994

A statistical procedure is developed to estimate the relative difference between two parameters each obtained from either true model or approximate model. Double sample procedure is applied to find the additional number of simulation runs satisfying the preassigned absolute precision of the confidence interval. Two types of parameters, mean and standard deviation, are considered as the performance measures and tried to show the validity of the model by examining both queues and inventory systems. In each system it is assumed that there are three distinct means and their own standard deviations and they form the simultaneous confidence intervals but with control in the sense that the absolute precision for each confidence interval is bounded on the limits with preassigned confidence level. The results of this study may contribute to some situations, for instance, first, we need a statistical method to compare the effectiveness between two alternatives, second, we find the adquate number of replications with any level of absolute precision to avoid the unrealistic cost of running simulation models, third, we are interested in analyzing the standard deviation of the output measure, ..., etc.

• 응용통계연구
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• 제2권1호
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• pp.18-34
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• 1989

서로 같은 분산을 가지며 정규분포를 따르는 4개의 처리평균의 대응비교에 관한 연구로서, 삼중 t-분포를 이용하여 동시포함 범위 확률값이 정확히 $1-\alpha$를 갖는 통계적 계산방법과 기법을 고찰하였다. 이 기법을 이용하여 처리사이의 표본 갯수를 변화시켜 대응되는 정확한 신뢰구간을 구하며 기존의 신뢰구간의 길이 비교, 실험적 오차 비, 효율성을 조사하였다.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.325-337
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• 1993

This paper propose two test statistics which enable us to proceed the variable selection in Fisher's linear discriminant function for the case of heterogeneous discrimination with equal training sample size. Simultaneous confidence intervals associated with the test are also given. These are exact and approximate results. The latter is based upon an approximation of a linear sum of Wishart distributions with unequal scale matrices. Using simulated sampling experiments, powers of the two tests have been tabulated, and power comparisons have been made between them.