• Journal of the Korean Data and Information Science Society
• /
• 제11권1호
• /
• pp.37-45
• /
• 2000

Consider the problem of estimating a $p{\times}1$ mean vector ${\underline{\theta}}(p{\geq}4)$ under the quadratic loss, based on a sample ${\underline{x}_{1}},\;{\cdots}{\underline{x}_{n}}$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}\;{\underline{\theta}}\;-\;{\bar{\theta}}{\underline{1}}\;{\parallel}$ is known, where ${\bar{\theta}}=(1/p){\sum_{i=1}^p}{\theta}_i$ and $\underline{1}$ is the column vector of ones.

• 통합자연과학논문집
• /
• 제10권1호
• /
• pp.33-39
• /
• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

• Kyungpook Mathematical Journal
• /
• 제16권1호
• /
• pp.135-140
• /
• 1976

• Communications for Statistical Applications and Methods
• /
• 제7권3호
• /
• pp.767-772
• /
• 2000

Zellner(1994) introduced the notion of a balanced loss function in the context of a general liner model to reflect both goodness of fit and precision of estimation. We study the perspective of unifying a variety of results both frequentist and Bayesian from Poisson distributions. We show that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for Poisson distribution.

• Journal of the Korean Data and Information Science Society
• /
• 제22권6호
• /
• pp.1251-1256
• /
• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• East Asian mathematical journal
• /
• 제40권1호
• /
• pp.95-107
• /
• 2024

Let K be an imaginary quadratic field with ring of integers 𝓞_K and N be a positive integer. By K_(N) we mean the ray class field of K modulo N𝓞_K. In this paper, for each prime p of K relatively prime to N𝓞_K we explicitly describe the action of the Artin symbol (${\frac{K_{(N)}/K}{p}}$) on special values of modular functions of level N. Furthermore, we extend the Kronecker congruence relation for the elliptic modular function j to some modular functions of higher level.

• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.13-19
• /
• 1995

This paper considers model robust accelerated life test plans for estimating the logmean or percentile of product lige which is exponentially distributed. A linear relationship between the log mean life and the stress is assumed as usual, while the true relationship is quadratic. Optimum plans are then obtained by minimizing asymptotic mean squared error of maximum likelihood estimator of the log mean life.

• 한국정보처리학회:학술대회논문집
• /
• 한국정보처리학회 2006년도 춘계학술발표대회
• /
• pp.23-26
• /
• 2006

기존의 데이터 마이닝 예측 기법 중 회귀분석은 학습 단계에서 생성된 모델을 변경 없이 새로운 데이터에 적용하였다. 그러나 시계열 데이터에 모델 변경 없이 동일하게 적용하면 시간이 지남에 따라 정확도가 낮아지는 단점이 있다. 따라서 이 논문에서는 시간에 따라 변화하는 시계열데이터의 특성을 고려하여 점진적으로 회귀 모델을 갱신하는 기법을 제안한다. 이 기법은 입력되는 모든 데이터를 회귀 모델에 적용하여 점진적으로 모델을 갱신한다. 제안된 기법의 타당성은 RME(Relative Mean Error)와 RMSE(Root Mean Square Error)를 이용하여 측정하였다. 정확도 측정 실험 결과 제안 기법인 IMQR(Incremental Multiple Quadratic Regression) 기법이 MLR(Multiple Linear Regression), MQR(Multiple Quadratic Regression), SVR(Support Vector Regression) 기법에 비해 RME 가 평균 2%, RMSE 가 평균 0.02 정도 우수한 결과를 얻었다.

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.257-266
• /
• 1995

Consider a p-variate $(p \geq 4)$ normal distribution with mean $\b{\theta}$ and identity covariance matrix. For estimating $\b{\theta}$ under a quadratic loss we investigate the behavior of risks of Stein-type estimators which shrink the usual estimator toward the mean of observations. By using concavity of the function appearing in the shrinkage factor together with new expectation identities for noncentral chi-squared random variables, a characterization of estimators with nondecreasing risk is obtained.

• Journal of the Korean Data and Information Science Society
• /
• 제28권2호
• /
• pp.435-442
• /
• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}$ (p ${\geq}$ 3) under the quadratic loss from multi-variate normal population. We find a James-Stein type estimator which shrinks towards the projection vectors when the underlying distribution is that of a variance mixture of normals. In this case, the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is known where K is a projection vector with rank(K) = q. The class of this type estimator is quite general to include the class of the estimators proposed by Merchand and Giri (1993). We can derive the class and obtain the optimal type estimator. Also, this research can be applied to the simple and multiple regression model in the case of rank(K) ${\geq}2$.