• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.539-544
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• 2005

In this paper, we propose the one-step least squares method based on the squared differences to estimate the parameters of the variogram used for spatial data modelling, and discuss its asymptotic efficiency. The proposed method does not require to specify lags of interest and partition lags, so that we can delete the subjectiveness and ambiguity originated from the lag selection in estimating spatial dependence.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.653-657
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• 2005

Eigenstructure of a spatial design matrix of Matheron's variogram estimator in $R^1$ is derived. It is shown that the spatial design matrix in $R^1$ with n/2$\le$h < n has a nice spectral decomposition. The mean, variance, and covariance of this estimator are obtained using the eigenvalues of a spatial design matrix. We also found that the lower bound and the upper bound of the normalized Matheron's variogram estimator.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.173-183
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• 2005

The Box-Cox power transformation is generally used for variance stabilization. Recently, Shin and Kang (2001) showed, under the Box-Cox transformation, invariant properties to the original model under the large mean and relatively small variance assumptions in time series analysis. In this paper we obtain some invariant properties in spatial statistics. Spatial statistics, Invariant Property, Variogram, Box-Cox power Transformation.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.269-273
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• 2003

We consider an efficient parametric estimation method of spatial dependence in weak stationary processes. Spatial dependence is modeled through variogram and correlogram. Most of parametric estimation methods of correlogram use two step method; nonparametric estimation and parametric integration. We bind these two steps into one step by using GEE method instead of least squares type optimization. Our one step method is more efficient statistically and gives a clear interpretation of related concepts used in traditional two step methods.

• Journal of Korean Society of Forest Science
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• v.101 no.2
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• pp.203-212
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• 2012

This study aims to test presence of spatial autocorrelation of burn severity in Uljin and Youngduk areas burned in 2011. SPOT satellite images were used to compute the NDVI representing burn severity, and NDVI values were sampled for 5,000 randomly dispersed points for each site. Spatial autocorrelations of sampled NDVI values were analyzed with Moran's I and Variogram models. Moran's I values of burn severity in Uljin and Youngduk areas were 0.7745 and 0.7968, respectively, indicating presence of strong spatial autocorrelations. On the basis of Variogram and changes of Moran's I values by lag class, ideal sampling distance were proposed, which were 566-2,151 m for Uljin and 272-402 m for Youngduk. It was recommended to apply these ranges of sampling distance in flexible corresponding to Anisotropic characteristics of burned areas.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.1
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• pp.91-98
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• 2016

In order to apply Kriging methods for geostatistics of spatial data, an estimation of spatial coherency functions is required priorly based on the spatial distance between measurement points. In the study, the typical coherency functions, such as semi-variogram, homeogram, and covariance function, were estimated using the national geoid model. The test area consisting of 2°×2° and the Unified Control Points (UCPs) within the area were chosen as sampling measurements of the geoid. Based on the distance between the control points, a total of 100 sampling points were grouped into distinct pairs and assigned into a bin. Empirical values, which were calculated with each of the spatial coherency functions, resulted out as a wave model of a semi-variogram for the best quality of fit. Both of homeogram and covariance functions were better fitted into the exponential model. In the future, the methods of various Kriging and the functions of estimated spatial coherency need to be studied to verify the prediction accuracy and to calculate the Mean Squared Prediction Error (MSPE).

• Korean Journal of Soil Science and Fertilizer
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• v.17 no.4
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• pp.319-324
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• 1984

Spatial variability of sand, silt, and clay contents on Hwadong SiCL and Jungdong SL was studied by using geostatistical concept. The measurements were made within a $33{\times}14m^2$ area at the nodes of 2 by 2m grids. The validity of all assumptions (stationarity, variogram models, etc.) was proved by Jack-knifing procedure and frequency distribution performed on the original data grids. The variogram of sand content on Hwadong SiCL was different from the linear model and that of clay content of Jungdong SL the linear and the spherical model in calculation of both kriged values and kriged variances in identification of its choice for simplicity.

• Economic and Environmental Geology
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• v.27 no.1
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• pp.81-91
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• 1994

There has been considerable research dealing with the influence of surface roughness along surfaces of rock discontinuities in relation to the peak shear strength of rock masses. Concepts accepted recently for measuring such strength include estimation of a roughness coefficient such as developed by Barton's studies. The method for estimation the Joint Roughness Coefficient (JRC) value of a measured roughness profile is subjective. The aim of this research is to estimate the JRC value of the roughness of a surface profile in a rock mass system using an objective method. The study of roughness of surfaces has included measurement of fractal geometric characteristics. Once the irregularity of the surface has been described by the fractal dimension, the spatial variation of the surface irregularities can be described using variogram and drift analysis. An empirical relationships between the roughness profiles of selected JRC ranges and their fractal dimension with variogram and drift were derived. The application of analyses of fractal dimension, variogram and drift was novel for the analysis of roughness profiles. Also, an empirical equation was applied to experimental data.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.423-432
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• 2003

The data observed at different positions are called the estimate of interested variable at new observation point on the Kriging utilize the space estimate technique, in which case there is correlation spatially. In this paper we provide the estimate for Variogram and Kriging methods as a field of kriging theory and dealt with actually measured data. And at the same time we forecast the amount of ozone that was not measured at this point by Kriging method and compared Ordinary Kriging method with Inverse Distance Kriging method.

• Korean Journal of Soil Science and Fertilizer
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• v.16 no.4
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• pp.305-310
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• 1983

Spatial variability of infiltration rates of 96 samples from Hwadong SiCL was studied by using geostatistical concepts. The measurement was made at the nodes of the regular grid consisting of 12 rows and 8 columns. Sample spacing within rows and columns was 3 and 2 meters, respectively. This study illustrated the use of variogram as a tool to identify the degree of dependency of the infiltration rate on the distance between pairs of measurements and how to take advantage of this dependency. Fractile diagram showed that the distribution of observation was approximately normal. The range of the variogram was about 7.4 meters. The minimum number of samples necessary to reproduce the results similar to the 96 measured values was 8 to 10. Coefficients of theoretical variogram function for computing kriged values and kriged varionces of nuogget effect, slope, and range were 0.444 cm/day, 0.003 cm/day, and 7.4 m, respectively.