• Journal of the Korean Mathematical Society
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• v.58 no.1
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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.

• Journal of Korea Trade
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• v.23 no.2
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• pp.110-126
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• 2019

Purpose - This paper examines the recently realized continuous volatility and discrete jumps of US Dollar/Euro returns using the frequency of five minute returns spanning the period from February 2010 through February 2018with periodicity filters. Design/Methodology - This paper adopts the nonparametric estimation. The realized volatility and Realized Outlying Weighted variations show non-Gaussian, fat-tailed, and leptokurtic distributions. Some significant volatility jumps in returns occurred from 2010 through 2018, and the very exceptionally large and irregular jumps occurred around 2010-2011, after the EU financial crisis, and 2015-2016. The outliers occurred somewhat frequently around the years of 2015 and 2016. Originality/value - When we include periodicity filters of volatility such as MAD, Short Half Scale, and WSD, the five minute returns of US Dollar/Euro exchange rates have smaller daily jump probabilities by 20-30% than when we do not include the periodicity filters of volatility. Thus, when we consider the periodicity filters of volatility such as MAD, Short Half Scale, and WSD, the five minute returns of US Dollar/Euro have considerably smaller jump probabilities.

• Journal of Korea Association of Health Promotion
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• v.2 no.1
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• pp.1-8
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• 2004

Background : Since 2001 the Korean Association of Health Promotion has attempted to establish her own reference valves that can be used in her all fifteen branch laboratories instead of using those adapted from the published data or there commended data by the reagent companies supplied as inserts. However, the previous two reference values derived from the statistics(year 2001 and 2002) were need to adjust to apply to actual practice. Besides there was an unavoidable situation that the reagent has to be changed to other companies in 2002 that creates another statistical problem. Subsequently, the third attempt to derive the reference ranges of tests in KAHP to solve those problems and define common)v acceptable reference ranges was done and and reported here. Methods : Al1 the results performed during January 2, 2003 through September 30, 2003 were collected in Excel tile format. All the data include dthe necessary information such as age and sex. The age was grouped in six; baby(0-3y), children(4-l2y), adolescent(13-l8y), adult(19-S4y), younger elderly (65-79y),old elderly(oyer 80y), with references of statistics in medical informatics and WHO classification. The data were statistically analyzed with SAS 6.04 for-Gaussian distribution as the previous two occasions. None of the tests showed Gaussian distribution. These procedures had been repeated twice or three times after trimming out the results lying outside three standard deviations. Though, all the tests showed non-Gaussian distribution. Subsequently, the reference ranges were defined in the range from the point of lower 2.5% to the point of higher 97.5 %. And in case the lower range could be "0", the reference ranges were defined in the range of 0 to 95%.Results : The reference ranges of most of 56 test items were newly assigned. Also with adaptation of the recommendation of WHO etc. on fasting blood sugar, hemoglobin, cholesterol. Among these there were eight tests that needed reference ranges by the age groups and nine tests by the sex. Conclusions : The third attempt will credit more the reference range of all15 laboratories of Korean Association of Health Promotion, which will be essential part of the better service to the patient and clients to visit KAHP.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.889-899
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• 2017

Independent component analysis is a multivariate approach to separate mixed signals into original signals. It is the most widely used method of blind source separation technique. ICA uses linear transformations such as principal component analysis and factor analysis, but differs in that ICA requires statistical independence and non-Gaussian assumptions of original signals. PCA have a natural ordering based on cumulative proportion of explained variance; howerver, ICA algorithms cannot identify the unique optimal ordering of the components. It is meaningful to set order because major components can be used for further analysis such as clustering and low-dimensional graphs. In this paper, we compare the performance of several criteria to determine the order of the components. Kurtosis, absolute value of kurtosis, negentropy, Kolmogorov-Smirnov statistic and sum of squared coefficients are considered. The criteria are evaluated by their ability to classify known groups. Two types of data are analyzed for illustration.

• Smart Structures and Systems
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• v.32 no.4
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• pp.267-279
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• 2023

Data modelling and interpretation for structural health monitoring (SHM) field data are critical for evaluating structural performance and quantifying the vulnerability of infrastructure systems. In order to improve the data modelling accuracy, and extend the application range from data regression analysis to out-of-sample forecasting analysis, an improved most likely heteroscedastic Gaussian process (iMLHGP) methodology is proposed in this study by the incorporation of the outof-sample forecasting algorithm. The proposed iMLHGP method overcomes this limitation of constant variance of Gaussian process (GP), and can be used for estimating non-stationary typhoon-induced response statistics with high volatility. The first attempt at performing data regression and forecasting analysis on structural responses using the proposed iMLHGP method has been presented by applying it to real-world filed SHM data from an instrumented cable-stay bridge during typhoon events. Uncertainty quantification and correlation analysis were also carried out to investigate the influence of typhoons on bridge strain data. Results show that the iMLHGP method has high accuracy in both regression and out-of-sample forecasting. The iMLHGP framework takes both data heteroscedasticity and accurate analytical processing of noise variance (replace with a point estimation on the most likely value) into account to avoid the intensive computational effort. According to uncertainty quantification and correlation analysis results, the uncertainties of strain measurements are affected by both traffic and wind speed. The overall change of bridge strain is affected by temperature, and the local fluctuation is greatly affected by wind speed in typhoon conditions.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.371-399
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• 2006

The theoretical background and capabilities of the developed program, SAR-CWF, for stochastic analysis of 3D reinforced-concrete shear wall-frame structures subject to seismic excitations is presented. Incremental stiffness and strength properties of system members are modeled by extended Roufaiel-Meyer hysteretic relation for bending while shear deformations for walls by Origin-Oriented hysteretic model. For the critical height of shear-walls, division to sub-elements is performed. Different yield capacities with respect to positive and negative bending, finite extensions of plastic hinges and P-${\delta}$ effects are considered while strength deterioration is controlled by accumulated hysteretic energy. Simulated strong motions are obtained from a Gaussian white-noise filtered through Kanai-Tajimi filter. Dynamic equations of motion for the system are formed according to constitutive and compatibility relations and then inserted into equivalent It$\hat{o}$-Stratonovich stochastic differential equations. A system reduction scheme based on the series expansion of eigen-modes of the undamaged structure is implemented. Time histories of seismic response statistics are obtained by utilizing the computer programs developed for different types of structures.

• Journal of Power System Engineering
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• v.4 no.2
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• pp.40-45
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• 2000

Some engineering materials are often known to have considerable spatial variation in their resisting strength and other properties. The objective of this study is to investigate the averaging effect and the applicability of extremal statistic for the statistical size effect. In the present study, it is assumed that the material property is a stationary random process in space. The theoretical autocorrelation function of the material strength are discussed for several correlation lengths. And, in order to investigate the statistical size effect, the material properties was simulated by using the non-Gaussian random process method. The material properties were plotted on the Weibull probability papers. The main results are summarized as follows: The autocorrelation function of the material properties are almost independent of the averaging length. The variance decreases with increasing the averaging length. As correlation length is smaller, the slope is larger. And also, it was found that Weibull statistics based on the weakest-link model could not explain the spatial variation of material properties with respect to the size effect satisfactory.

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• Geomechanics and Engineering
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• v.3 no.3
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• pp.169-188
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• 2011

Response of buried flexible pipe-soil system is studied, through numerical analysis, with respect to deflection and buckling in a spatially varying soil media. In numerical modeling procedure, soil parameters are modeled as two-dimensional non-Gaussian homogeneous random field using Cholesky decomposition technique. Numerical analysis is performed using random field theory combined with finite difference numerical code FLAC 5.0 (2D). Monte Carlo simulations are performed to obtain the statistics, i.e., mean and variance of deflection and circumferential (buckling) stresses of buried flexible pipe-soil system in a spatially varying soil media. Results are compared and discussed in the light of available analytical solutions as well as conventional numerical procedures in which soil parameters are considered as uniformly constant. The statistical information obtained from Monte Carlo simulations is further utilized for the reliability analysis of buried flexible pipe-soil system with respect to deflection and buckling. The results of the reliability analysis clearly demonstrate the influence of extent of variation and spatial correlation structure of soil parameters on the performance assessment of buried flexible pipe-soil systems, which is not well captured in conventional procedures.

• Proceedings of the KOSOMBE Conference
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• v.1991 no.11
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• pp.44-47
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• 1991

There exists a transform trellis code that is optimal for stationary Gaussian sources and the squared-error distortion measure at all rates. In this paper, we train an asymptotically optimal version of such a code to obtain one which is matched better to the statistics of real world data. The training algorithm uses the M-algorithm to search the trellis codebook and the LBG-algorithm to update the trellis codebook. To adapt the codebook for the varying input data. we use two gain-adaptive methods. The gain-adaptive scheme 1, which normalizes input block data by its gain factor, is applied to images at rate 0.5 bits/pixel. When each block is encoded at the same rate, the nonstationarity among the block variances leads to a variation in the resulting distortion from one block to another. To alleviate the non-uniformity among the encoded image, we design four clusters from the block power, in which each cluster has its own trellis codebook and different rates. The rate of each cluster is assigned through requiring a constant distortion per-letter. This gain-adaptive scheme 2 produces good visual and measurable quality at low rates.