• 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 Korean Data and Information Science Society
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• v.17 no.3
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• pp.805-809
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• 2006

In this paper a shrinkage estimator for the measure of dispersion of the inverse Gaussian distribution with known mean is proposed. Also we compare the relative bias and relative efficiency of the proposed estimator with respect to minimum variance unbiased estimator.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.625-636
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• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.657-667
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• 2006

The concept of entropy, introduced in communication theory by Shannon (1948) as a measure of uncertainty, is of prime interest in information-theoretic statistics. This paper considers the minimum variance unbiased estimation for the maximum entropy of the transformed inverse Gaussian random variable by $Y=X^{-1/2}$. The properties of the derived UMVU estimator is investigated.

• Journal of the Korean Statistical Society
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• v.7 no.2
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• pp.95-98
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• 1978

This note deals with the estimations of the variance of a normal distribution $N(\theta,c\theta^2)$ where c, the square of coefficient of variation is assumed to be known. This amounts to the estimation of $\theta^2$. The minimum variance estimator among all unbiased estimators linear in $\bar{x}^2$ and $s^2$ where $\bar{x}$ and $s^2$ are the sample mean and variance, respectively, and the minimum risk estimator in the class of all estimators linear in $\bar{x}^2$ and $s^2$ are obtained. It is shown that the suggested estimators are BAN.

• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.27-37
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• 1987

In life testing problem, many authors obtained the minimum variance unbiased estimator of $P_r$[X>Y] for the exponential family generally and conceptually. In this paper, we study the maximum likelihood estimator and minimum variance unbiased estimator of $P_r$[X>Y] in exponential X and normal Y.

• The Korean Journal of Applied Statistics
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• v.14 no.1
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• pp.13-24
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• 2001

In this paper, we investigated mean estimation methods in two-phase sampling. Under the fixed expected cost we reviewed the optimal sample sizes, minimum variances and approximate unbiased variance estimators for usual ratio estimator, stratified sample mean with proportional allocation and Rao's allocation of the second phase sample. Also we proposed combined ratio estimator, which uses both ratio estimation and stratification and derived optimal sample size, minimum variance and unbiased variance estimator. Through a limited simulation study, we compared estimators by design effects and came to know that ratio estimator is more efficient than stratified sample mean in some cases and inefficient in the other cases, but combined ratio estimator is more efficient than others in most cases.

• Journal of Korean Society for Quality Management
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• v.17 no.2
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• pp.55-63
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• 1989

In this paper we present the shrunken testing estimator for the variance of normal population and we find the condition that can be used in seeking the situations in which the proposed estimator is superior to the minimum variance unbiased estimator.

• Journal of Korean Society for Quality Management
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• v.7 no.2
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• pp.7-10
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• 1979

In this paper the Rao-Blackwell and Lehmann-$Scheff{\acute{e}}$ Theorem are used to drive the minimum variance unbiased estimators of system reliability for a number of distributions when a system consists of n Components whose random life times are assumed to be independent and identically distributed. For the case of a negative exponential life time, we obtain the maximum likelihood estimator of the system reliability and compair it with minimum variance unbiased estimator of the system reliability.