• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.403-410
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• 2023

Two-Phase sampling, which was first introduced by Neyman (1938), has various applications in different forms. Variance estimation for two-phase sampling has been an important research topic because conventional variance estimators used in most softwares are not working. In this paper, we considered a variance estimation for two-phase sampling in which stratified two-stage cluster sampling designs are used in both phases. By defining a conditionally unbiased estimator of an approximate variance estimator, which is calculable when all elements in the first phase sample are observed, we propose an explicit form of variance estimator of the double expanded estimator for a two-phase sample. A small simulation study shows the proposed variance estimator has a negligible bias with small variance. The suggested variance estimator is also applicable to other linear estimators of the population total or mean if appropriate residuals are defined.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.

• The Korean Journal of Applied Statistics
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• v.15 no.1
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• pp.119-128
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• 2002

In this paper, we consider the HB estimators of small area means with repeated survey. mao and Yu(1994) considered small area model with repeated survey data and proposed empirical best linear unbiased estimators. We propose a hierachical Bayes version of Rao and Yu by assigning prior distributions for unknown hyperparameters. We illustrate our HB estimator using very popular data in small area problem and then compare the results with the estimator of Census Bureau and other estimators previously proposed.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.921-929
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• 2014

A bivariate exponential distribution with a location parameter is proposed as a model for a two-component shared load system with a guarantee time. Some statistical properties of the proposed model are investigated. The maximum likelihood estimators and uniformly minimum variance unbiased estimators of the parameters, mean time to failure, and the reliability function of system are obtained with unknown guarantee time. Simulation studies are given to illustrate the results.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1217-1222
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• 2011

In this paper, we show that any circular density can be closely approximated by an exponential family of distributions. Therefore we propose an exponential family of distributions as a new family of circular distributions, which is absolutely suitable to model any shape of circular distributions. In this family of circular distributions, the trigonometric moments are found to be the uniformly minimum variance unbiased estimators (UMVUEs) of the parameters of distribution. Simulation result and goodness of fit test using an asymmetric real data set show usefulness of the novel circular distribution.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.79-89
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• 2007

A test for normality introduced by Arizono and Ohta(1989) is based on fullback-Leibler discrimination information. The test statistic is derived from the discrimination information estimated using sample entropy of Vasicek(1976) and the maximum likelihood estimator of the variance. However, these estimators are biased and so it is reasonable to make use of unbiased estimators to accurately estimate the discrimination information. In this paper, Arizono-Ohta test for normality is improved. The derived test statistic is based on the bias-corrected entropy estimator and the uniformly minimum variance unbiased estimator of the variance. The properties of the improved KL test are investigated and Monte Carlo simulation is performed for power comparison.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.255-264
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• 2015

This paper addressed the problem of estimation of finite population mean in double sampling for stratification. This paper proposed a generalized ratio-cum-product type estimator of population mean. The bias and mean square error of the proposed estimator has been obtained upto the first degree of approximation. A particular member of the proposed generalized estimator was identified and studied from a comparison point of view. It is observed that the identified particular estimator is more efficient than usual unbiased estimator and Ige and Tripathi (1987) estimators. An empirical study was conducted in support of the theoretical findings.

• Survey Research
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• v.10 no.1
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• pp.155-168
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• 2009

As an efficient sampling design, stratified random sampling is often used when auxiliary information is available at the designing stage. Although one - per - stratum design is an efficient design that can be used when many auxiliary variables are available, it does not provide any unbiased variance estimator. With a two - per - stratum sample in which two elements are selected from each stratum, it is possible to obtain an unbiased variance estimator. However the loss of efficiency could be significant if any important stratification variable is missed. In this study, we investigated a sampling design that uses the all given auxiliary information and also permits an unbiased variance estimator suggested by Park and Fuller(2008). Through a simulation study, we compared several stratified random sampling and systematic sampling design. We also applied the proposed stratified sampling designs to 2007 youth panel data.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37B no.10
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• pp.912-920
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• 2012

In this paper, we derived a closed-form equation of a Best Linear Unbiased Estimator (BLUE) estimator for the 3 dimensional estimation of the position of the emitter based on the Time Difference of Arrival (TDOA) technique. The BLUE derived for the case of estimating 3 dimensional position of the emitter with 4 base stations or sensors, and for this purpose, we used an approximated equation of the TDOA hyperbola equation obtained from the first order Taylor-series after setting the reference points of the position. The derived equation can be used for any kind of noises which are uncorrelated in each other in the TOA measurement noises and for a white Gaussian noise also.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.669-683
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• 2006

Model-based methods are generally used for small area estimation. Recently Shin and Lee (2003) suggested a method which used spatial correlations between areas for data set including some auxiliary variables. However in case of absence of auxiliary variables, Direct estimator is used. Even though direct estimator is unbiased, the large variance of the estimator restricts the use for small area estimation. In this paper, we suggest new estimators which take into account spatial correlation when auxiliary variables are not available. We compared Direct estimator and the newly suggested estimators using MSE, MAE and MB.