• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.87-92
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• 1996

A regression model with nested erroe structure is considered. The regression model includes two error terms that are independent and normally distributed with zero means and constant variances. This error structure of the model gives correlated response variables. The distributions of variance components in the regression model with nested error structure are dervied by using theorems for quadratic forms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.101-107
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• 2000

In this paper we establish an upper bound for the estimation error variance of a continuous stream with a stationary variogram V which is assumed to be of the r-Holder type (Lipschitzian) on [-d, d]. Functional properties for the mapping ${\xi}(t):=E[(X-X(t))^2]$, $t{\in}[0,d]$, are also given.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.10
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• pp.1-6
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• 1997

This paper presents the theoretical derivaion relating and image correlationcoeffcient capable of assessing image quality, with phase-error variance in antenna aperture domain. We show that when the phase-error variance of a range bin selected as an adaptive beamformer is known, the quality of the reconstructed image is predictable and moreover, the resultant correlation coeffcient is obviously greater than the derive dlower boudn. To support the derivation, real data are used for image formation where the dominant scatterer algorithm (DSA) is applied for phase compensations.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.459-471
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• 2002

In applications using a linear regression model with nested error structure, one might be interested in making inferences concerning variance components. This article proposes approximate confidence intervals on the variance component of the primary level in a simple linear regression model with an unbalanced nested error structure. The intervals are compared using computer simulation and recommendations are provided for selecting an appropriate interval.

• Journal of the Korea Society for Simulation
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• v.10 no.4
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• pp.41-50
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• 2001

When optimizing a complex system by determining the optimum condition of the system parameters of interest, we often employ the process of estimating the unknown objective function, which is assumed to be a second order spline function. In doing so, we normally use common random numbers for different set of the controllable factors resulting in more accurate parameter estimation for the objective function. In this paper, we will show some mathematical result for the analysis of variance when using common random numbers in terms of the regression error, the residual error and the pure error terms. In fact, if we can realize the special structure of the covariance matrix of the error terms, we can use the result of analysis of variance for the uncorrelated experiments only by applying minor changes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.9
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• pp.909-917
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• 1992

This paper proposes the realization of state-space digital filters with minimum output error variance. The algorithm is transforms of controllability and observability gramian in linear time invariant systems by weighted function and can improve performance of the digital filters by reducing the put error variance for state space coeffient variation. A numerical example shows that algorithm structure has much lower output error variance than that of other four structures(canonical, parallel, statistical sensitivity, balanced).

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.553-566
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• 2003

In many cases, the measurement error variances may be functions of the unknown true values or related covariates. This paper considers design-based estimators of the parameters of these variance functions based on the within-unit sample variances. This paper devotes to: (1) define an error scale factor $\delta$; (2) develop estimators of the parameters of the linear measurement error variance function of the true values under large-sample and small-error conditions; (3) use propensity methods to adjust survey weights to account for possible selection effects at the replicate level. The proposed methods are applied to medical examination data from the U.S. Third National Health and Nutrition Examination Survey (NHANES III).

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.75-78
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• 2003

Those who are interested in making inferences concerning linear combination of variance components in a simple linear regression model with unbalanced nested error structure can use the confidence intervals proposed in this paper. Two approximate confidence intervals for the sum of two variance components in the model are proposed. Simulation study is peformed to compare the methods.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.371-382
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• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.23-32
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• 2012

This paper deals with the bias and variance of regression coefficient estimators in a finite population. We derive approximate formulas for the bias, variance and mean square error of two estimators when we select a fixed-size inclusion probability proportional to the size sample and then estimate regression coefficients by the ordinary least square estimator as well as the weighted least square estimator based on the selected sample data. Necessary and sufficient conditions for the comparison of the two estimators in terms of variance and mean square error are suggested. In addition, a simple example is introduced to numerically compare the variance and mean square error of the two estimators.