• 대한수학회지
• /
• 제58권1호
• /
• pp.237-264
• /
• 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.

• Journal of the Korean Statistical Society
• /
• 제28권2호
• /
• pp.235-251
• /
• 1999

In this paper we examine extremal behavior of a $textsc{k}$th-order stationary Markov chain {X\ulcorner} by considering excesses over a high level which typically appear in clusters. Excesses over a high level within a cluster define a cluster damage, i.e., a normalized sum of all excesses within a cluster, and all excesses define a damage point process. Under some distributional assumptions for {X\ulcorner}, we prove convergence in distribution of the cluster damage and obtain a representation for the limiting cluster damage distribution which is well suited for simulation. We also derive formulas for the mean and the variance of the limiting cluster damage distribution. These results guarantee a compound Poisson limit for the damage point process, provided that it is strongly mixing.

• 한국경영과학회지
• /
• 제42권1호
• /
• pp.19-28
• /
• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• 응용통계연구
• /
• 제23권1호
• /
• pp.73-79
• /
• 2010

Missing values for unit root processes are imputed by the most recent observations. Treating the imputed observations as if they are complete ones, semiparametric unit root tests are extended to missing value situations. Also, an invariance principle for the partial sum process of the imputed observations is established under some mild conditions, which shows that the extended tests have the same limiting null distributions as those based on complete observations. The proposed tests are illustrated by analyzing an unequally spaced real data set.

• Journal of the Korean Statistical Society
• /
• 제21권2호
• /
• pp.167-177
• /
• 1992

In this paper, we investigate the limiting distribution of $M_n = max (X_1, X-2, \cdots, X_n)$ in the infinite moving average process ${X_t = \sum c_i Z_{t-i}}$ generated from i.i.d. negative binomial variables $Z_i$'s. While no limit result is possible, nonetheless asymptotic bounds are derived. We also present the tail behavior of $X_t$, i.e., weighted sum of i.i.d. random variables. This continues a study made by Rootzen (1986) for discrete innovation sequences.

• 응용통계연구
• /
• 제24권1호
• /
• pp.11-23
• /
• 2011

Robust unit root tests are developed for dynamic panels consisting of TAR processes. The test statistics are all based on diverse combinations of individual t-type tests for significance of TAR coefficients. Limiting null distributions are established. A Monte-Carlo experiment compares the proposed tests. The tests are applied to a panel data set of Canadian unemployment rates which show asymmetric features as well as having outliers.

• 열병합발전
• /
• 통권27호
• /
• pp.5-9
• /
• 2002

High pressure steam pipe in power plants is subjected to service conditions under which creep processes take place limiting the component's lifetime. To ensure a safe and economic operation it is necessary to get accurate information about the lifetime situation of single components as well as of the whole system. Careful evaluation is combined with FEM analysis, NDT, microstructure evaluation. Especially, 14MoV63 steel is used as material for main steam pipe for 30 years old power plants. In service inspections have shown an increasing number of cracks and creep cavities beside stress concentration parts. A detailed analysis came to the conclusion that lifetime has been consumed to a high degree, 80%level.

• Journal of the Korean Statistical Society
• /
• 제30권1호
• /
• pp.31-39
• /
• 2001

For estimating parameters of possibly nonlinear and/or non-stationary seasonal autoregressive(AR) processes, we introduce a new instrumental variable method which use the direction vector of the regressors in the same period as an instrument. On the basis of the new estimator, we propose new seasonal random walk tests whose limiting null distributions are standard normal regardless of the period of seasonality and types of mean adjustments. Monte-Carlo simulation shows that he powers of he proposed tests are better than those of the tests based on ordinary least squares estimator(OLSE).

• 대한수학회지
• /
• 제38권1호
• /
• pp.25-35
• /
• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• Journal of the Korean Statistical Society
• /
• 제36권4호
• /
• pp.447-456
• /
• 2007

On the basis of marginal likelihood of the residual vector which is free of nuisance mean parameters, we propose new Lagrange Multiplier seasonal unit root tests in seasonal autoregressive process. The limiting null distribution of the tests is the standardized ${\chi}^2-distribution$. A Monte-Carlo simulation shows the new tests are more powerful than the tests based on the ordinary least squares (OLS) estimator, especially for large number of seasons and short time spans.