• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.547-568
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• 2020

Modeling the statistical autocorrelations in spatial data is often achieved through the estimation of the variograms, where the selection of the appropriate valid variogram model, especially for small samples, is crucial for achieving precise spatial prediction results from kriging interpolations. To estimate such a variogram, we traditionally start by computing the empirical variogram (traditional Matheron or robust Cressie-Hawkins or kernel-based nonparametric approaches). In this article, we conduct numerical studies comparing the performance of these empirical variograms. In most situations, the nonparametric empirical variable nearest-neighbor (VNN) showed better performance than its competitors (Matheron, Cressie-Hawkins, and Nadaraya-Watson). The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with hole effect structure, fitted to the empirical VNN variogram is the most appropriate choice. This selected variogram is used with the ordinary kriging model to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.573-583
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• 2001

A condition in which the covariances of Matheron's variogram estimators are expressed in a simple form is reviewed. An asymptotic property of the covariances of the variogram estimators is examined, and a sufficient condition that guaranties the finiteness of the asymptotic variance of the normalized variogram estimators is provided.

• Korean Journal of Remote Sensing
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• v.22 no.5
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• pp.357-366
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• 2006

A traditional image analysis or classification method using satellite imagery is mostly based on the spectral information. However, the spatial information is more important according as the resolution is higher and spatial patterns are more complex. In this study, we attempted to compare and analyze the variogram properties of actual high resolution imageries mainly in the urban area. Through the several experiments, we have understood that the variogram is various according to a sensor type, spatial resolution, a location, a feature type, time, season and so on and shows the information related to a feature size. With simple modeling, we confirmed that the unique variogram types were shown unlike the classical variogram in case of small subsets. Based on the grasped variogram characteristics, we made a level index map for determining urban complexity or land-use classification. These results will become more and more important and be widely applied to the various fields of high-resolution imagery such as KOMPSAT-2 and KOMPSAT-3 which is scheduled to be launched.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.609-619
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• 2010

Geostatistical data among spatial data is analyzed in three stages: (1) variogram estimation, (2) model fitting for the estimated variograms and (3) spatial prediction using the fitted variogram model. It is very important to estimate the variograms properly as the first stage(i.e., variogram estimation) affects the next two stages. In general, the variogram is estimated with the moment estimator. To estimate the variogram, we have to decide the 'lag increment' or the 'number of lags'. However, there is no established rule for selecting the number of lags in estimating the variogram. The present paper proposes a method of choosing the optimal number of lags based on the PRESS statistic. To show the usefulness of the proposed method, we perform a small simulation study and show an empirical example with with air pollution data from Korea.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.109-123
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• 2005

Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

• Journal of Biosystems Engineering
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• v.39 no.4
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• pp.377-388
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• 2014

Purpose: Determining the spatial structure of data is important in understanding within-field variability for site-specific crop management. An understanding of the spatial structures present in the data may help illuminate interrelationships that are important in subsequent explanatory analyses, especially when site variables are correlated or are a combined response to multiple causative factors. Methods: In this study, correlation, principal component analysis, and single and nested variogram models were applied to soil electrical conductivity and chemical property data of two fields in central Missouri, USA. Results: Some variables that were highly correlated, or were strongly expressed in the same principal component, exhibited similar spatial ranges when fitted with a single variogram model. However, single variogram results were dependent on the active lag distance used, with short distances (30 m) required to fit short-range variability. Longer active lag distances only revealed long-range spatial components. Nested models generally yielded a better fit than single models for sensor-based conductivity data, where multiple scales of spatial structure were apparent. Gaussian-spherical nested models fit well to the data at both short (30 m) and long (300 m) active lag distances, generally capturing both short-range and long-range spatial components. As soil conductivity relates strongly to profile texture, we hypothesize that the short-range components may relate to the scale of erosion processes, while the long-range components are indicative of the scale of landscape morphology. Conclusion: In this study, we investigated the effect of changing active lag distance on the calculation of the range parameter. Future work investigating scale effects on other variogram parameters, including nugget and sill variances, may lead to better model selection and interpretation. Once this is achieved, separation of nested spatial components by factorial kriging may help to better define the correlations existing between spatial datasets.

• 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.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.327-336
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• 2004

Many researchers have used the robust variogram to reduce the effect of outliers in spatial data analysis. Recently it is known that estimating the variogram after replacing outliers is more efficient. In this paper, we suggest a new data cleaner for geostatistic data analysis and compare the efficiency of outlier cleaners.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.943-947
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• 2005

This study was intended to interpose an objection about the analysis of rainfall spatial distribution without a proper standard, and offer the improved approach using 1,he geostatistical analysis method to analyze it. For this, spatially distributed daily rainfall data sets were collected for 41 weather stations in study area, and variogram and correlation analysis were conducted. In the results of correlation analysis, it was found that the longer distance between the stations reduces the correlation of the rainfall data, and maltes the characteristics of the rainfall spatial distribution. The variogram analysis shows that correlation range was less than 50 km for the 17 daily rainfall data sets of total 91 sets. It says that it involves some rike, to determine the application method for rainfall spatial distribution without some qualifications, hence the Application standards of the Rainfall Spatial Distribution Analysis Technique, were essential and that was contingent on characteristics of rainfall and landscape.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.519-533
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• 2004

In this paper, we suggest quasi-likelihood estimation (QLE) method and its robust version in estimating spatial dependence modelled through variogram used for spatial data modelling. We compare the statistical characteristics of the estimators with other popular least squares estimators of parameters for variogram model by simulation study. The QLE method for estimating spatial dependence has the advantages that it does not need the concept of lags commonly required for least squares estimation methods as well as its statistical superiority. The QLE method also shows the statistical superiority to the other methods for the tested Gaussian and non-Gaussian spatial processes.