• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.647-652
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• 2010

By using a Malliavin calculus, we prove the central limit theorem on the power variation of the product of the unordered rectangles associated with a standard Brownian sheet.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.71-77
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• 2011

In this paper, asymptotic results are investigated when a parametric transformation is applied to ARMA models. The conditions are determined to ensure the strong consistency and the asymptotic normality of maximum likelihood estimators and the correct coverage probability of the forecast interval obtained by the transformation and backtransformation approach.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.287-292
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• 2012

Sample periodogram is widely known as an inconsistent estimator for true spectral density. We show that it becomes consistent when the true spectrum at the zero frequency (often known as long-run variance) equals zero. Asymptotic results for consistency of the periodogram as well as the rate of convergence are formally derived.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.1-11
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• 1996

The detection of multiple outliers in nonlinear regression models can be computationally not feasible. As a compromise approach, we consider the use of simulated annealing algorithm, an approximate approach to combinatorial optimization. We show that this method ensures convergence and works well in locating multiple outliers while reducing computational time.

• Journal of the Korean Statistical Society
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• v.4 no.1
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• pp.33-38
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• 1975

In the use of traditional autogressive linear equation, there are number of obvious limitations which may not be conventioanally neglected. This paper attempts to disclose some of them with respect to the assumptions made about error terms, conditions of convergence of the equation, prperties of estimators, etc.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.161-173
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• 2020

We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.

• Proceedings of the Korean Geotechical Society Conference
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• 1998.03a
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• pp.347-356
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• 1998

• Smart Structures and Systems
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• v.29 no.1
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• pp.17-28
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• 2022

The cable component of cable-stayed bridges is gradually impacted by weather conditions, vehicle loads, and material corrosion. The stayed cable is a critical load-carrying part that closely affects the operational stability of a cable-stayed bridge. Damaged cables might lead to the bridge collapse due to their tension capacity reduction. Thus, it is necessary to develop structural health monitoring (SHM) techniques that accurately identify damaged cables. In this work, a combinational identification method of three efficient techniques, including statistical analysis, clustering, and neural network models, is proposed to detect the damaged cable in a cable-stayed bridge. The measured dataset from the bridge was initially preprocessed to remove the outlier channels. Then, the theory and application of each technique for damage detection were introduced. In general, the statistical approach extracts the parameters representing the damage within time series, and the clustering approach identifies the outliers from the data signals as damaged members, while the deep learning approach uses the nonlinear data dependencies in SHM for the training model. The performance of these approaches in classifying the damaged cable was assessed, and the combinational identification method was obtained using the voting ensemble. Finally, the combination method was compared with an existing outlier detection algorithm, support vector machines (SVM). The results demonstrate that the proposed method is robust and provides higher accuracy for the damaged cable detection in the cable-stayed bridge.