• Korean Journal of Mathematics
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• v.25 no.1
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• pp.45-60
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• 2017

This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.835-844
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• 2003

A difficulty in spatial data analysis is to choose a suitable theoretical variogram. Generally mean squares error(MSE) is used as a criterion of selection. However researchers encounter the case that the values of MSE are almost the same whereas the estimates of parameters are different. In this case, the selection criterion based on MSE should take into account the parameter estimates. In this paper we study on the method of selecting a variogram using spatial correlation.

• East Asian mathematical journal
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• v.24 no.1
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• pp.21-25
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• 2008

The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.951-959
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• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.1017-1019
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• 1999

In this paper we present 2-dimensional image recovery method using Hadamard transform. Generally, the methods of Hadamard transform are more useful tools and much simplier than those of Fourier transform. The Hadamard transform can improve estimates when the detector is the source of noise. We take into account nonidealities in the system for the further improved image We also present the average mean square error(AMSE) associated with estimates with the results from computer simulations.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.9-20
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• 1997

Several methods are proposed for optimizing Fourier series estimators with respect to Mean Integrated Square Error metrics. Traditionally, such method have followed. one of two basic strategies; A stopping rules or the rules of determine multipliers. A central hypothesis of this study is that better estimates can be obtained by combining the two strategies. A new multiplier sequence is proposed, which used in conjunction with any of the stopping rules, is shown to improve the performance of estimator which relies solely on a stopping rule.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.736-740
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• 1991

EEG(Electroencephalogram) background signals can be represented as the sun of a conventional AR(Autoregressive) process and an innovation process, or a prediction error process. We have seen that conventional estimation techniques. such as least square estimates(LSE) or Gaussian maximum likelihood estimates(MLE-G) are optimal when the innovation process satisfies the Gaussian or presumed distribution. But when the data are contaminated by outliers, or artifacts, these assumptions are not met and conventional estimation techniques can badly fall and be strongly biased. It is known that EEG can be easily affected by artifacts. So we suggest a robust estimation technique which considerably performs well against those artifacts.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.259-261
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• 2008

GIS-based spatial data integration tasks have used exhaustive thematic maps generated from sparsely sampled data or satellite-based exhaustive data. Due to a simplification of reality and error in mapping procedures, such spatial data are usually imperfect and of different accuracy. The objective of this study is to carry out a sensitivity analysis in connection with input topographic data for landslide hazard mapping. Two different types of elevation estimates, elevation spot heights and a DEM from ASTER stereo images are considered. The geostatistical framework of kriging is applied for generating more reliable elevation estimates from both sparse elevation spot heights and exhaustive ASTER-based elevation values. The effects of different accuracy arising from different terrain-related maps on the prediction performance of landslide hazard are illustrated from a case study of Boeun, Korea.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.389-399
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• 2002

In order to examine whether the difference between two point estimates of population proportions is statistically significant, data analysts use two techniques. The first is to explore the overlap between two associated confidence intervals. Second method is to test the significance which is introduced at most statistical textbooks under the common assumptions of consistency, asymptotic normality, and asymptotic independence of the estimates. Under the null hypothesis which is two population proportions are equal, the pooled estimator of population proportion is preferred as a point estimator since two independent random samples are considered to be collected from one population. Hence as an alternative method, we could obtain another confidence interval of the difference of the population proportions with using the pooled estimate. We conclude that, among three methods, the overlapped method is under-estimated, and the difference of the population proportions method is over-estimated on the basis of the proposed method.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.201-217
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• 2000

The method of generalized estimating equations (GEE) has become very popular for the analysis of longitudinal data. We extend this work to the use of M-estimators; the resultant regression estimates are robust to heavy tailed errors and to outliers. The proposed method does not require correct specification of the dependence structure between observation, and allows for heterogeneity of the error. However, an estimate of the dependence structure may be incorporated, and if it is correct this guarantees a higher efficiency for the regression estimators. A goodness-of-fit test for checking the adequacy of the assumed M-estimation regression model is also provided. Simulation studies are conducted to show the finite-sample performance of the new methods. The proposed methods are applied to a real-life data set.