• Communications for Statistical Applications and Methods
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• 제20권1호
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• pp.85-96
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• 2013

A new bootstrap method combined with the stationary bootstrap of Politis and Romano (1994) and the classical residual-based bootstrap is applied to stationary autoregressive (AR) time series models. A stationary bootstrap procedure is implemented for the ordinary least squares estimator (OLSE), along with classical bootstrap residuals for estimated errors, and its large sample validity is proved. A finite sample study numerically compares the proposed bootstrap estimator with the estimator based on the classical residual-based bootstrapping. The study shows that the proposed bootstrapping is more effective in estimating the AR coefficients than the residual-based bootstrapping.

• 대한수학회지
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• 제58권1호
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Communications for Statistical Applications and Methods
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• 제22권5호
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• pp.495-506
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• 2015

Volatility is a variation measure in finance for returns of a financial instrument over time. GARCH models have been a popular tool to analyze volatility of financial time series data since Bollerslev (1986) and it is said that volatility is highly persistent when the sum of the estimated coefficients of the squared lagged returns and the lagged conditional variance terms in GARCH models is close to 1. Regarding persistence, numerous methods have been proposed to test if such persistency is due to volatility shifts in the market or natural fluctuation explained by stationary long-range dependence (LRD). Recently, Lee et al. (2015) proposed a residual-based cumulative sum (CUSUM) test statistic to test volatility shifts in GARCH models against LRD. We propose a bootstrap-based approach for the residual-based test and compare the sizes and powers of our bootstrap-based CUSUM test with the one in Lee et al. (2015) through simulation studies.

• 산업경영시스템학회지
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• 제25권2호
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• pp.50-56
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• 2002

In this study, we establish bootstrap control limits for EWMA chart by applying the bootstrap method, called resampling, which could not demand assumptions about pre-distribution when the process is skewed and/or the normality assumption is doubt. The results obtained in this study are summarized as follows : bootstrap EWMA control chart is developed for applying bootstrap method to EWMA chart, which is more sensitive to small shifts of process. With the purpose of eliminating a skewness of the resampling distribution, the bootstrap control limits are established by using a modified residual, and its performance is analyzed by ARL. It is shown that the bootstrap EWMA control chart developed in this study includes the properties of standard EWMA control chart that is sensitive to a small shift, and detects process in out of control more quickly than standard EWMA chart.

• 한국산업경영시스템학회:학술대회논문집
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• 한국산업경영시스템학회 2002년도 춘계학술대회
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• pp.365-370
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• 2002

In this study, according to MARMA(1,0) model which was suggested by Seppala, in case of existing autocorrelation in X control chart and EWMA control chart, the standard method and the non-parametric bootstrap method were compared and analysed using the bootstrap method which use the resampling prediction residual.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

• Journal of the Korean Data and Information Science Society
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• 제20권2호
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• pp.301-309
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• 2009

다차원척도법은 다변량분석에서 개체들을 대상으로 변수들을 측정한 후에 개체들 사이의 비유사성을 측정하고, 그 값들 혹은 반복하여 측정된 경우에는 그 값들의 평균을 이용하여 개체들을 저차원의 공간상에 도시화시켜 표현하는 분석방법이다. 본 논문에서는 응답자의 답변에 기초하여 비유사성을 측정할 때 이상치 또는 응답자의 답변이 불성실할 경우 발생하는 변이문제와 개체들 간의 거리에 대한 통계적 추론 문제에 붓스트랩 방법을 적용하는 내용을 다루고, 활용가능성을 무료일간지에 대한 유사성 평가 자료를 이용하여 실증적으로 분석하였다.

• Ocean and Polar Research
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• 제39권1호
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• pp.13-21
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• 2017

Temporal changes in the number of zooplankton species are important information for understanding basic characteristics and species diversity in marine ecosystems. The aim of the present study was to estimate the optimal monitoring frequency (OMF) to guarantee and predict the minimum number of species occurrences for studies concerning marine ecosystems. The OMF is estimated using the temporal number of zooplankton species through bi-weekly monitoring of zooplankton species data according to operational taxonomic units in the Tongyoung coastal sea. The optimal model comprises two terms, a constant (optimal mean) and a cosine function with a one-year period. The confidence interval (CI) range of the model with monitoring frequency was estimated using a bootstrap method. The CI range was used as a reference to estimate the optimal monitoring frequency. In general, the minimum monitoring frequency (numbers per year) directly depends on the target (acceptable) estimation error. When the acceptable error (range of the CI) increases, the monitoring frequency decreases because the large acceptable error signals a rough estimation. If the acceptable error (unit: number value) of the number of the zooplankton species is set to 3, the minimum monitoring frequency (times per year) is 24. The residual distribution of the model followed a normal distribution. This model can be applied for the estimation of the minimal monitoring frequency that satisfies the target error bounds, as this model provides an estimation of the error of the zooplankton species numbers with monitoring frequencies.