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Box-Cox Power Transformation Using R
Baek, Hoh Yoo The Basic Science Institute Chosun University 2020 조선자연과학논문집 Vol.13 No.2
If normality of an observed data is not a viable assumption, we can carry out normal-theory analyses by suitable transforming data. Power transformation by Box and Cox, one of the transformation methods, is derived the power which maximized the likelihood function. But it doesn't induces the closed form in mathematical analysis. In this paper, we compose some R the syntax of which is easier than other statistical packages for deriving the power with using numerical methods. Also, by using R, we show the transformed data approximately distributed the normal through Q-Q plot in univariate and bivariate cases with some examples. Finally, we present the value of a goodness-of-fit statistic(AD) and its p-value for normal distribution. In the similar procedure, this method can be extended to more than bivariate case.
A SEQUENCE OF IMPROVING LINDLEY'S ESTIMATOR OF A MULTIVARIATE NORMAL MEAN
Baek,Hoh Yoo 圓光大學校 1995 論文集 Vol.30 No.2
X=(X₁,ㆍㆍㆍ, X )'가 미지의 평균 θ=(θ₁,ㆍㆍㆍ, θ)'과 양정치 공분산 행렬 ∑p×p를 갖는 다변량 정규분포의 확률벡터라 하자. 이차 손실함수 ??=??에서 θ를 추정하는 문제를 생각한다. 본 논문에서는 ∑=??(σ²는 미지) 또는 ∑가 전부 미지일 때 Lindley 추정량상의 일련의 개량된 추정량들을 전개하고자 한다. Let ??=(X₁,ㆍㆍㆍ??)' have the multivariate normal distribution with unknown mean ??=(θ₁,ㆍㆍㆍ??)' and positive definite covariance matrix ??. Consider the problem of estimating ?? under the quadratic loss ??=??. In this paper we construct a sequence of improved estimators over Lindley's estimator(modified James-Stein estimator) when ∑=?? with unknown σ² or ∑ is completely unknown.
Lindley Type Estimators with the Known Norm
Baek, Hoh-Yoo The Korean Data and Information Science Society 2000 한국데이터정보과학회지 Vol.11 No.1
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.
Best Invariant Estimators In the Location Parameter Problem
Baek, Hoh Yoo 圓光大學校 基礎自然科學硏究所 1991 基礎科學硏究誌 Vol.10 No.2
本 論文에서의 分布族 이론의 성질과 어떤 變換群 하에서 存在되어지는 構造的 성질을 갖는 對應되는 推定量들을 보였다. 이러한 性質을 '不變性 原理'라고 한다. 이 原理를 位置 母數 문제에서 最量 位置 不變 推定量을 찾는 문제를 適用시키고 그 결과에 따르는 몇 가지에 例를 들었다.
Improved Estimators of the Mean in a Multivariate Normal Distribution
Baek, Hoh Yoo 圓光大學校 基礎自然科學硏究所 1994 基礎科學硏究誌 Vol.13 No.2
다변량 정규분포의 모평균을 추정하는 문제에서 James-Stein은 이차손실함수하에서 MIE보다 개량된 추정량을 발표한 이후 Lindly(1962)는 p≥4 에서 그것보다 개량된 추정량을 발표하였다. 본 논문에서는 Lindly의 형태의 추정량을 Guo와 Pal(1992)의 방법을 이용하여 그보다 좀 더 개량된 일련의 추정량들의 집합열을 전개하고자 한다.
SOME SEQUENCES OF IMPROVEMENT OVER LINDLEY TYPE ESTIMATOR
BAEK, HOH-YOO,HAN, KYOU-HWAN The Honam Mathematical Society 2004 호남수학학술지 Vol.26 No.2
In this paper, the problem of estimating a p-variate ($p{\geq}4$) normal mean vector is considered in a decision-theoretic setup. Using a simple property of the noncentral chi-square distribution, a sequence of smooth estimators dominating the Lindley type estimator has been produced and each improved estimator is better than previous one.
Lindley Type Estimation with Constrains on the Norm
Baek, Hoh-Yoo,Han, Kyou-Hwan The Honam Mathematical Society 2003 호남수학학술지 Vol.25 No.1
Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. 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 $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.