• East Asian mathematical journal
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• v.5 no.1
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• Asian-Australasian Journal of Animal Sciences
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• v.10 no.1
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• pp.70-74
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• 1997

Data on 2,571 lactation records of Nili-Ravi buffaloes from four institutional herds and four field recording centers were analyzed under an animal model to see the effect of season definition on the error variance of the fitted model. Herd-year-season(HYS) was the main fixed effect along with permanent environment, breeding value and residuals as the random effects. All known relationships among the animals were considered. The error variance differed for various HYS combinations. It was minimum when then months were not grouped into seasons. The four or Five season scenarios were better than the two season scenarios. The average number of lactations represented in a HYS combination varied widely from 6 to 28. Very few subclasses for a given HYS combination warrants the use of fewer seasons for animal model evaluation of buffaloes.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1223-1232
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• 2011

Tong and Wang's estimator (2005) is a new approach to estimate the error variance using least squares method such that a simple linear regression is asymptotically derived from Rice's lag- estimator (1984). Their estimator highly depends on the setting of a regressor and weights in small sample sizes. In this article, we propose a new approach via a local quadratic approximation to set regressors in a small sample case. We estimate the error variance as the intercept using a ridge regression because the regressors have the problem of multicollinearity. From the small simulation study, the performance of our approach with some existing methods is better in small sample cases and comparable in large cases. More research is required on unequally spaced points.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.693-698
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• 2000

Aspects of classical information theory, such as rate distortion theory, investigate how to encode and decode information from an independently identically distributed source so that the asymptotic distortion rate between the source and its quantized representation is minimized. However, in most natural dynamics, the source state is highly corrupted by disturbances, and the measurement contains the noise. In recent coder-estimator sequence is developed for state estimation problem based on observations transmitted with finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, the condition is that the observations must be coded and transmitted over a digital communication channel with finite capacity. However, coder-estimator sequence does not provide such a quantitative analysis as a variance for estimation error. In this paper, under the assumption that the estimation error is Gaussian distribution, a variance for coder-estimation sequence is proposed and its fitness is evaluated through simulations with a simple example.

• The Journal of the Korean dental association
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• v.57 no.8
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• pp.448-455
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• 2019

This study aims to apply the Generalizability Theory (G-theory) for estimation of reliability of evaluation scores between raters on Patient Dentist Interaction. Selecting a number of raters as multiple error sources, this study was analyzed the error sources caused by relative magnitude of error variances of interaction between the factors and proceeded with D-study based on the results of G-study for optimal determination of measurement condition. The estimated outcomes of variance component for accuracy among the Patient Dentist Interaction evaluation with G-theory showed that impact of error was the biggest influence factor in students. The second influence was the item effect, and the rater effect was relatively small. The Generalizability coefficients for case1 and case2 which were estimated through the D- study were calculated relatively low.

• Journal of Korea Water Resources Association
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• v.52 no.1
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• pp.11-19
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• 2019

In this study, the actual evapotranspiration products of Global Land Data Assimilation System (GLDAS), Global Land Evaporation Amsterdam Model (GLEAM) and MOD16, which are satellite- and reanalysis-based dataset, were validated at the flux tower sites (i.e., CFK and SMK) managed by Korea Institute of Hydrological Survey, and the uncertainty and correlation analysis were conducted using Triple Collocation (TC) method. The result of validation with the flux tower showed better agreement in the order of GLEAM> GLDAS>MOD16. At the result of three combinations (S1: flux tower vs. GLDAS vs. MOD16, S2: flux tower vs. GLDAS vs. GLEAM, S3: flux tower vs. GLEAM vs. MOD16), the order of best to worst is GLEAM, GLDAS, MOD16, and flux tower for CFK (GLDAS> GLEAM>MOD16>flux tower for SMK). Since the error variance and correlation coefficients of the flux tower show relatively worse performance in TC analysis than the other products, By applying TC method to three products (GLDAS vs. GLEAM vs. MOD16), the uncertainty of each dataset were evaluated at the Korean Peninsula, As a results, the GLDAS and GLEAM performed reasonable performance (low error variance and high correlation coefficient), whereas results of MOD16 showed high error variance and low correlation coefficient at the cropland.

• Journal of Korean Society for Quality Management
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• v.23 no.1
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• pp.95-105
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• 1995

The error structure of nonlinearized technological growth models, such as, the Pearl curve, the Gompertz curve and the Wei bull growth curve, has zero mean and a constant variance over time. Transformed models, however, like the linearized Fisher-Pry model. the linearized Gompertz growth curve, and the linearized Weibull growth curve have increasing variance from t = 0 to the inflection point.

• Journal of Korean Society for Quality Management
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• v.12 no.2
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• pp.33-36
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• 1984

This paper is concerned with the optimal replacement policy of auto-scale with increasing error-variance. This optimization model is to minimize the sum of the cost of defective and excess weight allowance for a target value. The numerical example for the proposed problem is solved by Golden-Section Search and Simpsons's rule.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• 한국정보통신설비학회:학술대회논문집
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• 2008.08a
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• pp.186-189
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• 2008

In order to estimate cell images, high-performance electron microscopes are used nowadays. In this paper, we propose a new simple, fast and efficient method for real-time automatic focusing in electron microscopes. The proposed algorithm is based on the prediction-error variance, and demonstrates its feasibility by using extensive experiments. This method is fast, easy to implement, accurate, and not demanding on computation time.