• Proceedings of the Optical Society of Korea Conference
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• 2005.02a
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• pp.346-347
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• 2005

• Journal of the Optical Society of Korea
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• v.16 no.4
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• pp.372-380
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• 2012

The optical method Digital Speckle Correlation Measurement (DSCM) has been extensively applied due its capability to measure the entire displacement field over a body surface. A formula of displacement measurement errors by the gradient-based DSCM method was derived. The errors were found to explicitly relate to the image grayscale errors consisting of sub-pixel interpolation algorithm errors, image noise, and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of displacement measurement errors on the subset size was established when the subset deformation was rigid body translation and random image noise was dominant and it was confirmed by both the numerical and experimental results. In a gradient-based algorithm the basic assumption is rigid body translation of the interrogated subsets, however, this is in contradiction to the real circumstances where strains exist. Numerical and experimental results also indicated that, subset shape function mismatch was dominant when the order of the assumed subset shape function was lower than that of the actual subset deformation field and the power-law dependence clearly broke down. The power-law relationship further leads to a simple criterion for choosing a suitable subset size, image quality, sub-pixel algorithm, and subset shape function for DSCM.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.79-83
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• 2002

A phase III clinical trial of a new drug for neutropenia induced by chemotherapy is presented and consider adding random effects in crossover design which was used in the clinical study. The diagnostics for its heteroscedasticity based on score statistic is derived for detecting homoscedasticity of errors in crossover design. A small simulation study is peformed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.247-257
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• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.189-201
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• 1996

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the density. And in Section 3, we derive two approximation formulae for the tail probability, one by following Daniels'(1987) method and the other by following Lugannani and Rice's (1980). In Section 4, we represent some numerical examples which show that the errors are small even for small sample size.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.69-80
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• 1983

The purpose of this paper is to obtain representation of the mathematical special functions and the numerical values of the mean square errors for the quasi-ranges in random small smaples ($n \leq 30$) from the Weibull distribution with a shape and a scale parameters, and to estimate the scale parameter by use of unbiased estimator based on the quasi-range. It will be shown that the jackknife estimator of the range is worse than the range of random samples from the given distribution in the sense of the mean square error.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.415-428
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• 1999

In this paper, we study the saddlepoint approximations for the ratio of two independent sequences of random variables. In Section 2, we review the saddlepoint approximation to the probability density function. In section 3, we derive an saddlepoint approximation formular for the tail probability by following Daniels'(1987) method. In Section 4, we represent a numerical example which shows that the errors are small even for small sample size.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.4
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• pp.352-357
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• 2004

This paper studies the errors that associated with particle velocity and intensity in a space. We theoretically derived their bias error and random error. The analysis shows that the more samples do not always guarantee the better results. The random error of the velocity and intensity are increased when we have many samples. The characteristics of the amplification of the random error are analyzed in terms of the sample spacing. The amplification was found to be related to the spatial differential of random noise. The numerical simulations are performed to verify theoretical results.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.335-344
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• 2017

This paper discusses a method of analyzing data from split-plot experiments by projections. The assumed model for data has two experimental errors due to two different experimental sizes and some random components in treatment effects. Residual random models are constructed to obtain sums of squares due to random effects. Expectations of sums of squares are obtained by Hartley's synthesis. Estimable functions of fixed effects are discussed.

• The Journal of Engineering Geology
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• v.3 no.1
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• pp.39-49
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• 1993

Intrinsic random function of order k(IRF-k) was used to estimate groundwater levels of nonstationaav random functions. The accuracy of IRF-k was compared to that of ordraarv krigrng assuming that the data of groundwater levels compose a stafionarv random function. Cross validation and statistical errors show that IRF-k is superior to orcinarv '(riging for the estimation of water levels. IRF-k and ordinary kriging made different contour and 3-D surface maps. The maps of IRF-k are more accurate than those of ordinary kriging.