• 품질경영학회지
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• 제32권4호
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• pp.229-241
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• 2004

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.29-36
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• 1999

분할표 분석에서 승산비 (odds ratio)에 대한 추론은 중요하다. 이에 대한 정확한 추론은 비중심초기하(noncentral hypergeometric) 분포의 누적확률등의 계산이 요구되어 표본의 크기가 클 경우 많은 양의 계산과 계산시간이 요구되므로 StatXact 등의 프로그램을 이용하는 것이 일반적이다. 본 논문에서는 정확한 추론에 대한 대안적 방법으로 안부점 근사(saddlepoint approximation)의 결과를 이용한 점근적 추론법을 제시하였다. 이 방법은 비교적 소표본의 경우에도 정확한 추론의 결과와 일치하며, 기존의 정규근사를 이용한 방법에 비해 매우 뛰어난 정확도를 유지함을 예제를 통해 확인하였다.

• Journal of the Korean Statistical Society
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• 제18권1호
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• pp.46-61
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• 1989

This paper is concerned with the development of a nonparametric procedure for the statistical inference about the nonlinear regression parameters. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both under the null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.471-477
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• 2007

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.139-144
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• 1990

For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

• Journal of the Korean Statistical Society
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• 제33권1호
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• pp.1-24
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• 2004

This paper is concerned with statistical methods for multivariate data when the number p of variables is large compared to the sample size n. Such data appear typically in analysis of DNA microarrays, curve data, financial data, etc. However, there is little statistical theory for high dimensional data. On the other hand, there are some asymptotic results under the assumption that both and p tend to $\infty$, in some ratio p/n ${\rightarrow}$c. The results suggest that the new asymptotic results are more useful and insightful than the classical large sample asymptotics. The main purpose of this paper is to review some asymptotic results for high dimensional statistics as well as classical statistics under a high dimensional asymptotic framework.

• 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 Statistical Society
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• 제36권2호
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• pp.257-274
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• 2007

This paper considers the tests for the presence of smooth transition non-linearity in the partially nonstationary vector autoregressive model. The transition parameters cannot be identified under the null hypothesis of linearity, and therefore this paper develops the tests for smooth transition nonlinearity, the associated asymptotic theory and the bootstrap inference. The Monte Carlo simulation evidence shows that the bootstrap inference generates moderate size and power performances.

• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.527-538
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• 2019

This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.