• Journal of the Korea Society for Simulation
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• v.19 no.3
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• pp.119-125
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• 2010

The moving block bootstrap, the stationary bootstrap, and the threshold bootstrap are methods of simulation output analysis, which are applicable to autocorrelated data. These bootstrap methods assume the stationarity of data. However, bootstrap methods cannot work if the stationary assumption is not guaranteed because of seasonality or trends in data. In the simulation output analysis, threshold bootstrap method is the best in describing the autocorrelation structure of original data set. The threshold bootstrap makes the cycle based on threshold value. If we apply the bootstrap to seasonality data, we can get similar accuracy of the results. In this paper, we verify the possibility of applying the bootstrap to seasonal data.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.745-754
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• 2006

It has been shown that LAD estimates are more efficient than LS estimates when the error distribution is double exponential in AR(1) model. In order to explore the performance of LAD estimates one can use bootstrap approaches. In this paper we consider the efficiencies of bootstrap methods when we apply LAD estimates with highly variable data. Monte Carlo simulation results are given for comparing generalized bootstrap, stationary bootstrap and threshold bootstrap methods.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.755-767
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• 1997

Analyzing autocorrelated data set is still an open problem. Developing on easy and efficient method for severe positive correlated data set, which is common in simulation output, is vital for the simulation society. Bootstrap is on easy and powerful tool for constructing non-parametric inferential procedures in modern statistical data analysis. Conventional bootstrap algorithm requires iid assumption in the original data set. Proper choice of resampling units for generating replicates has much to do with the structure of the original data set, iid data or autocorrelated. In this paper, a new bootstrap resampling scheme is proposed to analyze the autocorrelated data set : the Threshold Bootstrap. A thorough literature search of bootstrap method focusing on the case of autocorrelated data set is also provided. Theoretical foundations of Threshold Bootstrap is studied and compared with other leading bootstrap sampling techniques for autocorrelated data sets. The performance of TB is reported using M/M/1 queueing model, else the comparison of other resampling techniques of ARMA data set is also reported.

• Korean Management Science Review
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• v.22 no.1
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• pp.15-26
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• 2005

The bootstrap is a method of computational inference that simulates the creation of new data by resampling from a single data set. We propose a new job for the bootstrap: generating inputs from one historical trace using Threshold Bootstrap. In this regard, the most important quality of bootstrap samples is that they be functionally indistinguishable from independent samples of the same stochastic process. We describe a quantitative measure of difference between two time series, and demonstrate the sensitivity of this measure for discriminating between two data generating processes. Utilizing this distance measure for the task of generating inputs, we show a way of tuning the bootstrap using a single observed trace. This application of the threshold bootstrap will be a powerful tool for Monte Carlo simulation. Monte Carlo simulation analysis relies on built-in input generators. These generators make unrealistic assumptions about independence and marginal distributions. The alternative source of inputs, historical trace data, though realistic by definition, provides only a single input stream for simulation. One benefit of our method would be expanding the number of inputs achieving reality by driving system models with actual historical input series. Another benefit might be the automatic generation of lifelike scenarios for the field of finance.

• Proceedings of the Korea Society for Simulation Conference
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• 1993.10a
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• pp.2-2
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• 1993

Inference for discrete event simulations usually relies on either independent replications or, if each simulation run is expensive, the method of batch means applied to a single replications. We present a new method, threshold bootstrap, which equals or exceeds the performance of independent replications or batch means. The method works by resampling runs of data created when a stationary time series crosses a threshold level, such as the sample mean of series. Computational results show that the threshold bootstrap matches or exceeds the performance of these alternative methods in estimating the standard deviation of the sample mean and producing valid confidence intervals.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.177-187
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• 2020

This article is concerned with the issue of forecasting and evaluation of threshold-asymmetric volatility models for time series of count data. In particular, threshold integer-valued models with conditional Poisson and conditional negative binomial distributions are highlighted. Based on the parametric bootstrap method, some evaluation measures are discussed in terms of one-step ahead forecasting. A parametric bootstrap procedure is explained from which directional measure, magnitude measure and expected cost of misclassification are discussed to evaluate competing models. The cholera data in Bangladesh from 1988 to 2016 is analyzed as a real application.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.05a
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• pp.169-169
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• 2001

With the aid of fast computing power, resampling techniques are being introduced for simulation output analysis (SOA). Autocorrelation among the output from discrete-event simulation prohibit the direct application of resampling schemes (Threshold bootstrap, Binary bootstrap, Stationary bootstrap, etc) extend its usage to time-series data such as simulation output. We present a new method for inference from a regenerative process, regenerative bootstrap, that equals or exceeds the performance of classical regenerative method and approximation regeneration techniques. Regenerative bootstrap saves computation time and overcomes the problem of scarce regeneration cycles. Computational results are provided using M/M/1 model.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.39-56
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• 2000

${\overline{X}}$ control chart has proven to be an effective tool to improve the product quality. Shewhart charts assume that the observations are independent and normally distributed. Under the presence of positive autocorrelation and severe skewness, the control limits are not accurate because assumptions are violated- Autocorrelation in process measurements results in frequent false alarms when standard control chats are applied in process monitoring. In this paper, Threshold Bootstrap and Moving Block Bootstrap are used for constructing a confidence interval of correlated observations. Monte Carlo simulation studies are conducted to compare the performance of the bootstrap methods and that of standard method for constructing control charts under several conditions.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.2
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• pp.65-73
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• 2013

In the simulation output analysis, bootstrap method is an applicable resampling technique to insufficient data which are not significant statistically. The moving block bootstrap, the stationary bootstrap, and the threshold bootstrap are typical bootstrap methods to be used for autocorrelated time series data. They are nonparametric methods for stationary time series data, which correctly describe the original data. In the simulation output analysis, however, we may not use them because of the non-stationarity in the data set caused by the trend such as increasing or decreasing. In these cases, we can get rid of the trend by differencing the data, which guarantees the stationarity. We can get the bootstrapped data from the differenced stationary data. Taking a reverse transform to the bootstrapped data, finally, we get the pseudo-samples for the original data. In this paper, we introduce the applicability of bootstrap methods to the time series data having trend, and then verify it through the statistical analyses.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.10a
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• pp.62-62
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• 1999

In this paper, we propose a new technique of estimating tail of steady-state queue length distribution; Pr(Q>q), fo ATM multiplexer. Pr(Q>q) is a fundamental measure of network congestion. Assessing Pr(Q>q) properly is crucial for design and control of ATM networks. Data traffic pattern of high-speed networks is highly correlated and bursty. Estimating Pr(Q>q) is very difficult because of correlation and burstiness. We estimate entropy(rate-function) using large deviation principles and threshold bootstrap. Simulation studies are conducted to compare the performance of an existing method and our new method.