• 한국조사연구학회:학술대회논문집
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• 한국조사연구학회 2002년도 추계학술대회 발표논문집
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• pp.255-274
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• 2002

We classify rotation sampling designs into two classes. The first class replaces sample units within the same rotation group while the second class replaces sample units between different rotation groups. The first class is specified by the three-way balanced design which is a multi-level version of previous balanced designs. We introduce an extended generalized composite estimator (EGCE) and derive its variance and mean squared error for each of the two classes of design, cooperating two types of correlations and three types of biases. Unbiased estimators are derived for difference between interview time biases, between recall time biases, and between rotation group biases. Using the variance and mean squared error, since any rotation design belongs to one of the two classes and the EGCE is a most general estimator for rotation design, we evaluate the efficiency of EGCE to simple weighted estimator and the effects of levels, design gaps, and rotation patterns on variance and mean squared error.

• Journal of the Korean Data and Information Science Society
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• 제16권2호
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• pp.371-382
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• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of the Korean Data and Information Science Society
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• 제20권3호
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• pp.577-585
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• 2009

So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.

• East Asian mathematical journal
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• 제5권1호
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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.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.165-181
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• 2010

This paper presents some chain ratio-type estimators for estimating finite population variance using two auxiliary variables in two phase sampling set up. The expressions for biases and mean squared errors of the suggested c1asses of estimators are given. Asymptotic optimum estimators(AOE's) in each class are identified with their approximate mean squared error formulae. The theoretical and empirical properties of the suggested classes of estimators are investigated. In the simulation study, we took a real dataset related to pulmonary disease available on the CD with the book by Rosner, (2005).

• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• 한국산학기술학회논문지
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• 제14권2호
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• pp.625-633
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• 2013

본 다중반응표면 최적화는 다수의 반응변수(품질특성치)를 동시에 고려하여, 입력변수의 최적 조건을 찾는 것을 목적으로 한다. 지금까지 다중반응표면 최적화를 위하여 다양한 방법이 제안되어 왔는데, 그 중 평균제곱오차 최소화법은 다수의 반응변수의 평균과 표준편차를 동시에 고려하여 최적화하는 방법이다. 이 방법은 기본적으로 평균과 표준편차가 동일한 가중치를 가지고 있다는 것을 전제로 하고 있다. 그러나 문제의 상황에 따라 평균과 표준편차에 서로 다른 가중치를 부여해야 하는 경우도 있다. 이에 본 논문에서는 기존의 평균제곱오차를 확대하여 평균과 표준편차에 서로 다른 가중치도 부여할 수 있도록 가중평균제곱오차 최소화법을 제안하고자 한다.

• 한국산학기술학회논문지
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• 제16권1호
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• pp.97-105
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• 2015

다중반응표면 최적화는 다수의 반응변수(품질특성치)를 최적화하는 입력변수의 조건을 찾는 것을 목적으로 한다. 다중반응표면 최적화를 위해 제안된 가중평균제곱오차(Weighted Mean Squared Error, WMSE) 최소화법은 평균제곱오차의 구성요소인 제곱편차와 분산에 서로 다른 가중치를 부여하는 방법이다. 지금까지 WMSE 최소화법과 관련하여, 개별 반응변수의 WMSE를 구성한 후 이들의 가중합을 최소화하는 가중합 기반 WMSE 최소화법이 제안되었다. 그러나 가중합 기반법은 목적함수 공간에서 볼록하지 않은 구간이 있고 이 구간에서 가장 선호되는 해가 존재할 경우 이 해를 찾아내지 못한다는 한계를 지니고 있다. 본 논문에서는 기존의 가중합 기반법의 한계점을 극복하기 위하여 Tchebycheff Metric 기반 WMSE 최소화법을 제안하고자 한다.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.249-259
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• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.285-292
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• 1999

In this paper we propose the several estimators of the Lorenz curve in the Pareto distribution and obtain the bias and the mean squared error for each estimator. We compare the proposed estimators with the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) in terms of the mean squared error (MSE) through Monte Carlo methods and discuss the results.