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

• Communications for Statistical Applications and Methods
• /
• v.23 no.2
• /
• pp.163-177
• /
• 2016

We consider a jump diffusion process for high-frequency financial asset data. We apply the stationary bootstrapping to construct a bootstrap test for jumps. First-order asymptotic validity is established for the stationary bootstrapping of the jump ratio test under the null hypothesis of no jump. Consistency of the stationary bootstrap test is proved under the alternative of jumps. A Monte-Carlo experiment shows the advantage of a stationary bootstrapping test over the test based on the normal asymptotic theory. The proposed bootstrap test is applied to construct continuous-jump decomposition of the daily realized variance of the KOSPI for the year 2008 of the world-wide financial crisis.

• Communications for Statistical Applications and Methods
• /
• v.22 no.5
• /
• pp.463-473
• /
• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• The Korean Journal of Applied Statistics
• /
• v.11 no.1
• /
• pp.151-161
• /
• 1998

We study the bootstrap interval estimation for survival function in the Koziol-Green model. We construct the approximate bootstrap confidence intervals for survival function and prove the strong consistency for the bootstrap estimator of survival function. Finally we show that the approximate bootstrap confidence intervals are better in terms of coverage probability than confidence intervals based on asymptotic normal distribution and transformations of survival function via Monte Carlo simulation study.

• Journal of the Korean Statistical Society
• /
• v.26 no.4
• /
• pp.543-554
• /
• 1997

A family of some capability indices { $C_{p}$(.alpha.,.beta.); .alpha..geq.0, .beta..geq.0}, containing the indices $C_{p}$, $C_{{pk}}$, $C_{{pm}}$, and $C_{{pmk}}$, has been defined by Vannman(1993) for the case of two-sided specification interval. By varying the parameters of the family various capability indices with suitable properties are obtained. We derive tha asymptotic distribution of the family { $C_{p}$(.alpha.,.beta.); .alpha..geq.0,.beta..geq.0} under general proper conditions. It is also shown that the bootstrap approximation to the distribution of the estimator $C_{p}$(.alpha., .beta.) is vaild for almost all sample sequences. These asymptotic distributions would be used in constructing some bootstrap confidence intervals.tervals.

• The Korean Journal of Applied Statistics
• /
• v.35 no.1
• /
• pp.1-17
• /
• 2022

We propose a test of consistency for two differentially private histograms using parametric bootstrap. The test can be applied when the original raw histograms are not available but only the differentially private histograms and the privacy level α are available. We also extend the test for the case where the privacy levels are different for different histograms. The resident population data of Korea and U.S in year 2020 are used to demonstrate the efficacy of the proposed test procedure. The proposed test controls the type I error rate at the nominal level and has a high power, while a conventional test procedure fails. While the differential privacy framework formally controls the risk of privacy leakage, the utility of such framework is questionable. This work also suggests that the power of a carefully designed test may be a viable measure of utility.

• Journal of Korean Society for Quality Management
• /
• v.32 no.4
• /
• pp.229-241
• /
• 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.

• Proceedings of the Korean Association for Survey Research Conference
• /
• 2006.06a
• /
• pp.131-159
• /
• 2006

This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

• Journal of Korean Institute of Industrial Engineers
• /
• v.36 no.1
• /
• pp.1-6
• /
• 2010

The Analytic Hierarchy Process (AHP) has been applied widely in various decision making fields. One of advantages of the AHP is the consistency test. However, it has several problems such as the limit of its concept, the limit of 9 scales and stern criteria, contradictory pairwise comparison. In this paper, we propose new criteria for the consistency with more realistic and ideal conditions. To derive the criteria, we conduct the simulation and use the bootstrap method, which is one of resampling techniques in the simulation area.

• Communications for Statistical Applications and Methods
• /
• v.10 no.3
• /
• pp.1047-1056
• /
• 2003

In this paper, we consider a modified bootstrap scheme for inference of the GPH estimator and establish the sup-norm consistency of the proposed bootstrapping.