• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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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 Statistical Society
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• v.29 no.4
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• pp.385-394
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• 2000

Jackknife variance estimation based on adjusted imputed values when nonresponse is nonrandom and follow-up data are available for a subsample of nonrespondents is provided. Both hot-deck and ratio imputation method are considered as imputation method. The performance of the proposed variance estimator under nonrandom response mechanism is investigated through numerical simulation.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.693-698
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• 2000

Aspects of classical information theory, such as rate distortion theory, investigate how to encode and decode information from an independently identically distributed source so that the asymptotic distortion rate between the source and its quantized representation is minimized. However, in most natural dynamics, the source state is highly corrupted by disturbances, and the measurement contains the noise. In recent coder-estimator sequence is developed for state estimation problem based on observations transmitted with finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, the condition is that the observations must be coded and transmitted over a digital communication channel with finite capacity. However, coder-estimator sequence does not provide such a quantitative analysis as a variance for estimation error. In this paper, under the assumption that the estimation error is Gaussian distribution, a variance for coder-estimation sequence is proposed and its fitness is evaluated through simulations with a simple example.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.501-508
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• 2003

Although the estimate of regression function is important, some have focused the variance estimation of error term in regression model. Different variance estimators perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are approximately satisfied so as to identify the best variance estimator for the given data. In this article, we suggest SHM estimator compared to LS estimator, which is common estimator using in parametric multiple regression analysis. Moreover, a combined estimator of variance, VEM, is suggested. In the simulation study it is shown that VEM performs well in practice.

• Nuclear Engineering and Technology
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• v.55 no.11
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• pp.4228-4237
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• 2023

The Improved Deterministic Truncation of Monte Carlo (iDTMC) is a powerful acceleration and variance reduction scheme in the Monte Carlo analysis. The concept of the iDTMC method and correlated sampling-based real variance estimation are briefly introduced. Moreover, the application of the iterative scheme to the correlated sampling is discussed. The iDTMC method is utilized in a 3-dimensional small modular reactor (SMR) model problem. The real variances of burnup-dependent criticality and power distribution are evaluated and compared with the ones obtained from 30 independent iDTMC calculations. The impact of the inactive cycles on the correlated sampling is also evaluated to investigate the consistency of the correlated sample scheme. In addition, numerical performances and sensitivity analysis on the real variance estimation are performed in view of the figure of merit of the iDTMC method. The numerical results show that the correlated sampling accurately estimates the real variances with high computational efficiencies.

• 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.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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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.

• Proceedings of the Korean Association for Survey Research Conference
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• 2007.11a
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• pp.213-230
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• 2007

Although the response model has been frequently applied to nonresponse weighting adjustment or imputation, the estimation under callbacks has been relatively underdeveloped in the response model. The estimation method using the response probability is developed under callbacks. A replication method for the estimation of the variance of the proposed estimation is also developed. Since the true response probability is usually unknown, we study the estimation of the response probability. Finally, we propose an estimator under callbacks using the ratio imputation as well as the response probability. The simulation study illustrates our techniques.

• Proceedings of the Korean Association for Survey Research Conference
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• 2001.04a
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• pp.59-71
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• 2001

We investigate design-based variance estimation methods of homogeneous linear estimator for population total under stratified multi-stage sampling. One method is unbiasedly estimating the first stage variance and the second stage variance separately in each stratum. And another is sub-sampling method that estimating the first stage variance only by using sub-sample selected from the second stage sample so that resulting estimator is unbiased for the total variance. The first is useful when the second stage unbiased estimator is available and the second is when the second stage variance is not estimable. For each case, we proposed a form of non-negative unbiased variance estimator. We expect the proposed variance estimation methods can be effectively used for many practical surveys.

• Survey Research
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• v.2 no.1
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• pp.59-71
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• 2001

We investigate design-based variance estimation methods of homogeneous linear estimator for population total under stratified multi-stage sampling. One method is unbiasedly estimating the first stage variance and the second stage variance separately in each stratum. And another is sub-sampling method that estimating the first stage variance only by using sub-sample selected from the second stage sample so that resulting estimator is unbiased for the total variance. The first is useful when the second stage unbiased estimator is available and the second is when the second stage variance is not estimable. For each case, we proposed a form of non-negative unbiased variance estimator. We expect the proposed variance estimation methods can be effectively used for many practical surveys.