• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.131-142
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• 1999

Estimators for domains and approximate estimators of their variance are derived using post-stratified complex sample. Furthermore we propose an adjusted variance estimator of a domain mean in case of considering the post-stratified complex sample as simple random sample. A simulation study based on the data of Farm Household Economy Survey is presented to compare variance estimators numerically. From the study we showed that our adjusted variance estimator compensate for the under-estimation problem considerably.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.233-238
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• 2005

S${\"{a}}$rndal (1996) and Knottnerus (2003) had a critical look at the well known variance estimator of Sen (1953) and Yates and Grundy (1953) in probability proportional to size sampling. In this paper, we point out that although their approaches can avoid the difficulties in variance estimation with respect to the joint probabilities, there exist the disadvantages in practice. Also, we describe a sampling procedure available in statistical software that are useful for the variance estimation.

• 응용통계연구
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• 제14권1호
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• pp.13-24
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• 2001

이중추출에서 모평균 추정방법을 고찰하였다. 전통적으로 널리 쓰이는 비추정량과 회귀추정량 그리고 비례배분 및 Rao 배분을 한 후의 층화평균에 대하여 주어진 기대 비용에서 최적의 표본수, 최소분산 및 분산추정량을 살펴보았다. 또한 비추정 및 층화의 효과를 모두 내포하는 결합비 추정량을 제안하고 주어진 기대 비용에서 최적의 표본수 및 최소분산을 유도하였고 분산추정량을 구하였다. 그리고 제한된 모의실험을 통하여 비추정량, 층화평균 및 결합비 추정량의 효율을 비교하였다. 모의실험 결과 비추정량과 층화평균은 경우에 따라 효율이 다르게 나타난 반면, 결합비 추정량은 대체로 두 방법보다 효율이 우수하게 나타나 결합비 추정량이 이중추출에 유용하게 쓰일 수 있음을 보였다.

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.929-937
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• 2003

Kernel type estimations of discontinuity point at an unknown location in regression function or its derivatives have been developed. It is known that the discontinuity point estimator based on $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a zero value at the point 0 makes a poor asymptotic behavior. Further, the asymptotic variance of $Gasser-M\ddot{u}ller$ regression estimator in the random design case is 1.5 times larger that the one in the corresponding fixed design case, while those two are identical for the local polynomial regression estimator. Although $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a non-zero value at the point 0 for the modification is used, computer simulation show that this phenomenon is also appeared in the discontinuity point estimation.

• Journal of the Korean Statistical Society
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• 제7권2호
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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 the Korean Statistical Society
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• 제34권3호
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• pp.219-233
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• 2005

The 3-way balanced multi-level rotation design has been discussed (Park Kim and Kim, 2003), where the 3-way balancing is done on interview time, in monthly sample and rotation group and recall time. A greater advantage of 3-way balanced design is accomplished by an estimator. To obtain the advantage, we generalized previous generalized composite estimator (GCE). We call this as l-step GCE. The variance of the l-step GCE's of various characteristics of interest are presented. Also, we provide the coefficients which minimize the variance of the l-step GCE. Minimizing a weighted sum of variances of all concerned estimators of interest, we drive one set of the compromise coefficient of l-step GCE's to preserve additivity of estimates.

• Journal of the Korean Statistical Society
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• 제35권1호
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• pp.105-114
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• 2006

In this paper we propose a simple and computationally attractive difference-based variance estimator in nonparametric regression models with multivariate predictors. We show that the estimator achieves $n^{-1/2}$ rate of convergence for regression functions with only a first derivative when d, the dimension of the predictor, is less than or equal to 4. When d > 4, the rate turns out to be $n^{-4/(d+4)}$ under the first derivative condition for the regression functions. A numerical study suggests that the proposed estimator has a good finite sample performance.

• Journal of the Korean Data and Information Science Society
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• 제26권2호
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• pp.377-385
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• 2015

표본조사에서 무응답이 발생한 개체에 대해 재조사 실시한 후 보조변수를 사용한 회귀추정의 형태를 가지는 추정량을 제시하고 복제치 기법을 이용한 분산추정량을 연구한다. 또한 응답여부에 따른 응답확률의 모수적 추론방법도 함께 제시한다. 재조사 후 모평균에 대하여 불편성을 만족하고 효율이 좋은 추정량과 일치성을 가지는 분산추정량을 이론적으로 연구하고 모의실험을 통하여 연구의 타당성을 입증한다.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1223-1232
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• 2011

Tong and Wang's estimator (2005) is a new approach to estimate the error variance using least squares method such that a simple linear regression is asymptotically derived from Rice's lag- estimator (1984). Their estimator highly depends on the setting of a regressor and weights in small sample sizes. In this article, we propose a new approach via a local quadratic approximation to set regressors in a small sample case. We estimate the error variance as the intercept using a ridge regression because the regressors have the problem of multicollinearity. From the small simulation study, the performance of our approach with some existing methods is better in small sample cases and comparable in large cases. More research is required on unequally spaced points.