• 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.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.743-750
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• 2012

In this study, we propose definitions for the one-sided variance for asymmetric distribution. We consider to apply the one-sided variance to the construction to define modified $C_{pk}$, which is a definition for the process capability index for the asymmetric process distribution. Then we consider to obtain the consistent estimation for the one-sided variance and to apply to the various industrial fields.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.317-329
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• 2006

In the problem of estimating the error variance in the balanced fixed- effects one-way analysis of variance (ANOVA) model, Ghosh (1994) proposed hierarchical Bayes estimators and raised a conjecture for which all of his hierarchical Bayes estimators are admissible. In this paper we prove this conjecture is true by representing one-way ANOVA model to the distributional form of a multiparameter exponential family.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.296-302
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• 1995

When heteroscedasticity occurs in random effects linear model, the error variance may depend on the values of one or more of the explanatory variables or on other relevant quantities such as time or spatial ordering. In this paper we derive a score test as a diagnostic tool for detecting non-constant error variance in random effefts linear model based on the model expansion on error variance. This score test is compared to loglikelihood ratio test.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.315-324
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• 2002

For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.

• 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.

• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.33-45
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• 2016

Variance components should be estimated based on mean change when the mean of the observations drift gradually over time. Consistent estimators for the variance components are studied for a particular modeling situation with some underlying functions or drift. We propose a new variance estimator with Fourier estimation of variations. The consistency of the proposed estimator is proved asymptotically. The proposed procedures are studied and compared empirically with the variance estimators removing trends. The result shows that our variance estimator has a smaller mean square error and depends on drift patterns. We estimate and apply the variance to Nile River flow data and resting state fMRI data.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.305-313
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• 2002

Regarding to inference about a scalar measure of internal scatter of Ρ-variate normal population, this paper considers an interval estimation of the generalized variance, │$\Sigma$│. Due to complicate sampling distribution, fully parametric frequentist approach for the interval estimation is not available and thus Bayesian method is pursued to calculate the highest probability density (HPD) interval for the generalized variance. It is seen that the marginal posterior distribution of the generalized variance is intractable, and hence a weighted Monte Carlo method, a variant of Chen and Shao (1999) method, is developed to calculate the HPD interval of the generalized variance. Necessary theories involved in the method and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed method.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.563-568
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• 1995

It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.

• Korean Journal of Hydrosciences
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• v.4
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• pp.51-63
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• 1993

This study is to verify the applicability of statistical models in predicting flood frequency at the stage gaging stations of which the flow is under natural condition in the Han River basin. The results of the study show that the statistical flood frequency models were proven to be fairly reasonable to apply in practice, and also were compared with sampling variance to calibrate the statistical efficiency of the estimators of the T year floods Q(T) by two different flood frequency models. As a result, it was showed that for return periods greater than about T = 10 years the annual exceedance series estimators of Q(T) has smaller sampling variance than the annual maximum series estimators. It was showed that for the range of return periods the partial duration series estimators of !(T) has smaller sampling variance than the annual maximum series estimate only if the POT model contains at least 2N(N : record length) items or more in order to estimate Q(T) more efficiently than the ANNMAX model.