• 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.

• Communications for Statistical Applications and Methods
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• v.28 no.4
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• pp.315-327
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• 2021

The Spatial Autoregressive (SAR) models have drawn considerable attention in recent econometrics literature because of their capability to model the spatial spill overs in a feasible way. While considering the Bayesian analysis of these models, one may face the problem of lack of robustness with respect to underlying prior assumptions. The generalized Bayes estimators provide a viable alternative to incorporate prior belief and are more robust with respect to underlying prior assumptions. The present paper considers the SAR model with a set of linear restrictions binding the regression coefficients and derives restricted generalized Bayes estimator for the coefficients vector. The minimaxity of the restricted generalized Bayes estimator has been established. Using a simulation study, it has been demonstrated that the estimator dominates the restricted least squares as well as restricted Stein rule estimators.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.419-432
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• 1997

A robust estimator for interpolating spatially distributed regionalized variables is introduced. It reduces outlier effects on ob-taining correlation between spatial lags and the correlation between spatial lags and the corresponding semi-variances and produces a significaantly improved semivariogram com-pared with those of conventional estimators. This estimator is applied to a field experimental data set.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.669-683
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• 2006

Model-based methods are generally used for small area estimation. Recently Shin and Lee (2003) suggested a method which used spatial correlations between areas for data set including some auxiliary variables. However in case of absence of auxiliary variables, Direct estimator is used. Even though direct estimator is unbiased, the large variance of the estimator restricts the use for small area estimation. In this paper, we suggest new estimators which take into account spatial correlation when auxiliary variables are not available. We compared Direct estimator and the newly suggested estimators using MSE, MAE and MB.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.375-382
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• 2010

In this study, we propose a robust estimator of the multivariate location parameter by means of the spatial median based on data trimming which extending trimmed mean in the univariate setup. The trimming quantity of this estimator is determined by the bootstrap method, and its covariance matrix is estimated by using the double bootstrap method. This extends the work of Jhun et al. (1993) to the multivariate case. Monte Carlo study shows that the proposed trimmed spatial median estimator yields better efficiency than a spatial median, while its covariance matrix based on double bootstrap overcomes the under-estimating problem occurred on single bootstrap method.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.349-356
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• 2010

The ordinary least squares based estimator of the disturbance variance in a regression model for spatial panel data is shown to be asymptotically unbiased and weakly consistent in the context of SAR(1), SMA(1) and SARMA(1,1)-disturbances when there is measurement error in the regressor matrix.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.265-275
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• 2009

This paper considers a linear regression model with a spatial autoregressive disturbance with ill-posed data and proposes the generalized maximum entropy(GME) estimator of regression coefficients. The performance of this estimator is investigated via Monte Carlo experiments. The results show that the GME estimator provides efficient and robust estimate for the unknown parameter.

• 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.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.543-556
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• 2015

We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.659-667
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• 2009

Recently Song and Cheon (2006) and Cheon and Lim (2009) developed the generalized maximum entropy(GME) estimator to solve ill-posed problems for the regression coefficients in the simple panel model. The models discussed consider the individual and a spatial autoregressive disturbance effects. However, in many application in economics the data may contain nested groupings. This paper considers a two-way error component model with nested groupings for the ill-posed data and proposes the GME estimator of the unknown parameters. The performance of this estimator is compared with the existing methods on the simulated dataset. The results indicate that the GME method performs the best in estimating the unknown parameters in terms of its quality when the data are ill-posed.