• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.609-633
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• 2014

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.281-292
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• 1995

In this paper the concept of strong mixing is extended to random fields, and an invariance principle is obtained for stationary strong mixing random fields.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.243-248
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• 1995

In this article we show that a class of random coefficient autoregressive processes including the NEAR (New exponential autoregressive) process has the strong mixing property in the sense of Rosenblatt with mixing order decaying to zero. The result can be used to construct model free prediction interval for the future observation in the NEAR processes.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.81-93
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• 2015

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.195-210
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• 2007

This paper develops a consistent nonparametric test for Granger causality in the context of strong-mixing process, which covers a large class of stationary processes including ARMA and ARCH models. The previously proposed tests require absolute regularity ($\beta$-mixing) more stringent than the strong-mixing condition. We prove the consistency of the test under a high level assumption on the approximation error of U statistic by its projection. Due to the sample splitting, the test statistic we propose is asymptotically normally distributed under the null.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.479-486
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• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.345-354
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• 2004

Boente and Fraiman [2] studied robust nonparametric estimators for regression or autoregression problems when the observations exhibit serial dependence. They established strong consistency of two families of M-type robust equivariant estimators for $\phi$-mixing processes. In this paper we extend their results to weaker $\alpha$$alpha$-mixing processes.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.51-54
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• 2002

When a cold HPSI (High Pressure Safety Injection) fluid associated with an design basis accident, such as LOCA (Loss of Coolant Accident), enters the cold legs of a stagnated primary coolant loop, thermal stratification phenomena will arise due to incomplete mixing. If the stratified flow enters a reactor pressure vessel downcomer, severe thermal stresses are created in a radiation embrittled vessel wall by local overcooling. Previous thermal-mixing analyses have assumed that the thermal stratification phenomena generated in stagnated loop of a partially stagnated coolant loop are neutralized in the vessel downcomer by strong flow from unstagnated loop. On the basis of these reasons, this paper presents the thermal-mixing analysis results in order to identify the fact that the cold plume generated in the vessel downcomer due to the thermal stratification phenomena of the stagnated loop is affected by the strong flow of the unstagnated loop.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.328-335
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• 2002

In this study, experiments were performed to investigate the characteristics of flame stabilization of the LFG mixing gas. LFG has merely half heating value compared with liquified natural gas but can be greatly utilized as a commercial fuel. In order to use LFG in practical combustors, Webbe Index and heating value of LFG mixing gas were adjusted by mixing LPG with LFG. The comparisons were conducted between CH$_4$and LFG mixing gas for searching the region of flame stabilization based upon the flame blowout at maximum fuel stream velocity. As a result, the flame stability of LFG mixing gas was not improved with that of CH$_4$in non-swirl and weak swirl diffusion flame. However, LFG mixing gas had wide flame stabilization region rather than CH$_4$with increasing ambient flow rate in strong swirl. It was also found that flame stability was affected by included quantity of inert gas such as CO$_2$in the weak swirl but by heating value of fuel in strong swirl.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.173-179
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• 2000

Interval prediction based on the empirical distribution function for the class of time series with time varying coefficients is discussed. To this end, strong mixing property of the model is shown and results due to Fotopoulos et. al.(1994) are employed. A simulation study is presented to assess the accuracy of the proposed interval predictor.