• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.95-103
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• 1993

Necessary and sufficient conditions for the equality between the best linear unbiased estimators in two linear models with different covariance matrices, $V_1 and V_2$, say, are derived. Various applications of this discovery are also given. Necessary and sufficient conditions for the equality between the best linear unbiased estimator and the ordinary least squares estimator are discussed related to this topic.

• The Mathematical Education
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• v.22 no.2
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• pp.27-29
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• 1984

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.69-79
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• 1996

• 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.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.2
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• pp.46-52
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• 2009

In this paper, the timing estimator based on the principle of the best linear unbiased estimator (BLUE) is proposed in OFDMA uplink systems. The proposed timing estimator exploits the phase information of the differential correlation between adjacent subcarriers. The differential correlation can extract the information about timing offset and mitigate the distortion of the signal caused by the frequency selectivity of channel. Compared with conventional methods, the proposed estimator shows more accurate capability in estimation. In addition, the estimator is hardly affected by the distortion caused by the frequency selectivity of channel. Simulation results confirm that the proposed estimator shows a small error mean and a relatively small error variance. In addition, the performance of the estimator is evaluated by means of SNR loss. It is shown by simulations that the SNR loss of the proposed estimator by estimation errors is less than 0.4 dB for the SNR values between 0 and 20 dB. This might indicate that the proposed estimator is suitable for the timing synchronization of multiple users in OFDMA uplink systems.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.153-161
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• 2009

We consider a logistic model with random effects as the superpopulation for estimating the small area pro-portions. The best linear unbiased predictor under linear mired model is popular in small area estimation. We use this type of estimator under logistic mixed motel for the small area proportions, on which the estimation of mean squared error is also discussed. Two kinds of estimation methods, the parametric bootstrap and the linear approximation will be compared through a Monte Carlo study in the respects of the normality assumption on the random effects distribution and also the magnitude of sample sizes on the approximation.

• The Korean Journal of Applied Statistics
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• v.15 no.1
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• pp.119-128
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• 2002

In this paper, we consider the HB estimators of small area means with repeated survey. mao and Yu(1994) considered small area model with repeated survey data and proposed empirical best linear unbiased estimators. We propose a hierachical Bayes version of Rao and Yu by assigning prior distributions for unknown hyperparameters. We illustrate our HB estimator using very popular data in small area problem and then compare the results with the estimator of Census Bureau and other estimators previously proposed.

• ETRI Journal
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• v.34 no.4
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• pp.511-517
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• 2012

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)-based wireless relay networks (WRNs). In this paper, a BLUE-based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy-based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cram$\acute{e}$r-Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal-to-noise ratio.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.799-803
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• 2003

We obtained the best linear unbiased estimator for the scale parameter of the generalized Pareto Distribution by the order statistics.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37B no.10
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• pp.912-920
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• 2012

In this paper, we derived a closed-form equation of a Best Linear Unbiased Estimator (BLUE) estimator for the 3 dimensional estimation of the position of the emitter based on the Time Difference of Arrival (TDOA) technique. The BLUE derived for the case of estimating 3 dimensional position of the emitter with 4 base stations or sensors, and for this purpose, we used an approximated equation of the TDOA hyperbola equation obtained from the first order Taylor-series after setting the reference points of the position. The derived equation can be used for any kind of noises which are uncorrelated in each other in the TOA measurement noises and for a white Gaussian noise also.