• Communications for Statistical Applications and Methods
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• 제22권1호
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• pp.81-93
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• 2015

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.341-357
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• 1999

Greenwich and Jahr-Schaffrath(1995) considered a new process incapability index(PII) $C_{pp}$, which modified the useful index $C^{\ast}_{pm}{$ for detecting assignable causes. The new index $C_{pp}$ provides an uncontaminated separation between information concerning the process accuracy and precision while this kind of information separation is not available with the $C^{\ast}_{pm}$ index. In this paper, we will study about the index $C_{pp}$ based on the bootstrap. First, we will prove the consistency of bootstrap deriving the bootstrap asymptotic distribution for our index $C_{pp}$. Moreover, with the consistency of bootstrap, we will construct six bootstrap confidence intervals and compare their performances. Some simulation results, comparison and analysis are provided. In particular, two STUD and ABC bootstrap methods perform significantly better.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.697-709
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• 2001

In this paper we study two vector-valued process capability indices $C_{p}$=($C_{px}$, $C_{py}$ ) and C/aub pm/=( $C_{pmx}$, $C_{pmy}$) considering process capability indices $C_{p}$ and $C_{pm}$ . First, two asymptotic distributions of plug-in estimators $C_{p}$=($C_{px}$, $C_{py}$ ) and $C_{pm}$ =) $C_{pmx}$, $C_{pmy}$) are derived.. With the asymptotic distributions, we propose asymptotic confidence regions for our indices. Next, obtaining the asymptotic distributions of two bootstrap estimators $C_{p}$=($C_{px}$, $C_{py}$ )and $C_{pm}$ =( $C_{pmx}$, $C_{pmy}$) with our bootstrap algorithm, we will provide the consistency of our bootstrap for statistical inference. Also, with the consistency of our bootstrap, we propose bootstrap asymptotic confidence regions for our indices. (no abstract, see full-text)see full-text)e full-text)

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.59-70
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• 1997

We introduce several estimators of the location and the scale parameters of the two-parameter exponential distribution, and then compare these estimators by the mean square error (MSE). Using the parametric bootstrap estimators and the delete-d jackknife, we obtain the bootstrap and the delete-d jackknife confidence intervals for the location and the scale parameters and compare the bootstrap confidence intervals with the delete-d jackknife confidence intervals by length and coverage probability through Monte Carlo method.

• Communications for Statistical Applications and Methods
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• 제19권3호
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• pp.405-414
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• 2012

층화확률추출은 모집단을 어떤 층화기준에 의해 여러 층으로 분할한 다음 각 층으로부터 독립적으로 표본을 임의추출하는 방법으로 여러 가지 장점을 가지고 있어 실제 조사에서 많이 활용되고 있다. 본 연구에서는 대규모 표본조사에서 많이 사용하고 있는 층화확률추출을 사용하여 추출된 표본을 통해 모평균에 대한 붓스트랩 추정량과 신뢰구간 및 가설검정 등 통계적 추론에 대하여 연구하였다. 층화모집단에서의 모평균의 추정량과 관련된 극한 분포이론들을 기초로 붓스트랩 일치성을 근거로 층화 모평균에 대해 표준 붓스트랩 방법, 백분위수 붓스트랩 방법, 스튜던트화 붓스트랩 방법을 활용한 신뢰구간과 붓스트랩 가설검정 방법을 제안하였으며, 모의실험을 통해 신뢰구간 추정 방법들의 유효성을 확인하였다.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.361-368
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• 1993

In recent years, kernel type estimates are abundant. In this paper, we propose a bandwidth selection method for kernel regression of fixed design based on bootstrap procedure. Mathematical properties of proposed bootstrap-based bandwidth selection method are discussed. Performance of the proposed method for small sample case is compared with that of cross-validation method via a simulation study.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.1-18
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• 1995

The generalized logit model of nominal type with random regressors is studied for bootstrapping. In particular, asymptotic normality and consistency of bootstrap model estimators are derived. It is shown that the bootstrap approximation to the distribution of the maximum likelihood estimators is valid for alsomt all sample sequences.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.183-195
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• 1995

For a distribution on the unit sphere, the set of eigenvectors of the second moment matrix is a conventional measure of orientation. Asymptotic confidence cones for eigenvector under the parametric assumptions for the underlying distributions and nonparametric confidence cones for eigenvector based on bootstrapping were proposed. In this paper, to reduce the level error of confidence cones for eigenvector, double bootstrap confidence cones based on prepivoting are considered, and the consistency of this method is discussed. We compare the perfomances of double bootstrap method with the others by Monte Carlo simulations.

• Journal of the Korean Data and Information Science Society
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• 제3권1호
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• pp.33-46
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• 1992

The set of eigenvectors of the second moment matrix and the mean vector are the measures of orientation for a distribution supported on the unit sphere. Bootstrap confidence cone for the eigenvector is constructed and the consistency of this method is discussed. The performance of our bootstrap cone for the eigenvector is compared with that of the asymptotic confidence cones for two measures under the parametric assumptions for the underlying distributions and that of the bootstrap cone for the mean vector by Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• 제15권1호
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• pp.1-8
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• 1986

The k-medians clustering method is considered to partition observations into k clusters. Consistency and advantage of bootstrap confidence sets of k optimal cluster centers are discussed. The k-medians and k-means clustering methods are compared by using actual data sets.