• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.681-695
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• 2012

In this paper, a family of estimators for the finite population variance investigated by Srivastava and Jhajj (1980) is studied under two different situations of random non-response considered by Tracy and Osahan (1994). Asymptotic expressions for the biases and mean squared errors of members of the proposed family are obtained; in addition, an asymptotic optimum estimator(AOE) is also identified. Estimators suggested by Singh and Joarder (1998) are shown to be members of the proposed family. A correction to the Singh and Joarder (1998) results is also presented.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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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).

• Proceedings of the Korean Association for Survey Research Conference
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• 2006.12a
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• pp.67-83
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• 2006

In successive sampling on two occasions the problem of estimating a finite population quantile has been considered. The theory developed aims at providing the optimum estimates by combining (i) three double sampling estimators viz. ratio-type, product-type and regression-type, from the matched portion of the sample and (ii) a simple quantile based on a random sample from the unmatched portion of the sample on the second occasion. The approximate variance formulae of the suggested estimators have been obtained. Optimal matching fraction is discussed. A simulation study is carried out in order to compare the three estimators and direct estimator. It is found that the performance of the regression-type estimator is the best among all the estimators discussed here.

• Journal of the Korean Statistical Society
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• v.36 no.4
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• pp.543-556
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• 2007

In successive sampling on two occasions the problem of estimating a finite population quantile has been considered. The theory developed aims at providing the optimum estimates by combining (i) three double sampling estimators viz. ratio-type, product-type and regression-type, from the matched portion of the sample and (ii) a simple quantile based on a random sample from the unmatched portion of the sample on the second occasion. The approximate variance formulae of the suggested estimators have been obtained. Optimal matching fraction is discussed. A simulation study is carried out in order to compare the three estimators and direct estimator. It is found that the performance of the regression-type estimator is the best among all the estimators discussed here.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.23-32
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• 2012

This paper deals with the bias and variance of regression coefficient estimators in a finite population. We derive approximate formulas for the bias, variance and mean square error of two estimators when we select a fixed-size inclusion probability proportional to the size sample and then estimate regression coefficients by the ordinary least square estimator as well as the weighted least square estimator based on the selected sample data. Necessary and sufficient conditions for the comparison of the two estimators in terms of variance and mean square error are suggested. In addition, a simple example is introduced to numerically compare the variance and mean square error of the two estimators.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.45-62
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• 2000

Rotation design is a sampling technique to reduce response burden and to estimate the population characteristics varying in time. Park and Kim(1999) discussed a generation of one-level rotation design which is called as {{{{r_1^m ~-r_2^m-1}}}} design has more applicable form than existing before. In the structure of {{{{r_1^m ~-r_2^m-1}}}} design, we derive the exact variances of generalized composite estimators for level, change and aggregate level characteristics of interest, and optimal coefficients minimizing their variances. Finally numerical examples are shown by the efficiency of alternative designs relative to widely used 4-8-4 rotation design. This is continuous work of Part Ⅰ studied by Park and Kim(1999).

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.2
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• pp.114-125
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• 2003

This paper proposes multivariate process capability indices (PCIs) for skewed populations using $T^2$rand modified process region approaches. The proposed methods are based on the multivariate version of a weighted standard deviation method which adjusts the variance-covariance matrix of quality characteristics and approximates the probability density function using several multivariate Journal distributions with the adjusted variance-covariance matrix. Performance of the proposed PCIs is investigated using Monte Carlo simulation, and finite sample properties of the estimators are studied by means of relative bias and mean square error.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.281-290
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• 2007

Linear estimator, a weighted sum of the sample observation, is commonly adopted to estimate the finite population parameters such as population totals in survey sampling. The weight for a sampled unit is often constructed by multiplying the base weight, which is the inverse of the first-order inclusion probability, by an adjustment term that takes into account of the auxiliary information obtained throughout the population. The linear estimator using the weight adjustment is often more efficient than the one using only the bare weight, but its valiance estimation is more complicated. We discuss variance estimation for a general class of weight-adjusted estimator. By identifying that the weight-adjusted estimator can be viewed as a function of estimated nuisance parameters, where the nuisance parameters were used to incorporate the auxiliary information, we derive a linearization of the weight-adjusted estimator using a Taylor expansion. The method proposed here is quite general and can be applied to wide class of the weight-adjusted estimators. Some examples and results from a simulation study are presented.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.263-274
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• 2010

Business survey index(BSI) is an economic forecasting index made on the basis of the past achievement of the company and enterpriser's plan and decision for the future. Even the index is very popular in economic situations, only a little research result is known to the public. In the paper we investigate statistical properties of BSI. We define population BSI in the finite population and estimate it unbiasedly. Also we derive the variance of the estimated BSI and its unbiased estimator. In addition, confidence interval of the estimated BSI is proposed. We asserte that confidence interval of the estimated BSI is more reasonable than the relative standard error.

• Survey Research
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• v.12 no.3
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• pp.49-62
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• 2011

In this paper we investigate design-based properties of both the ordinary least square estimator and the weighted least square estimator for regression coefficients in panel regression model. We derive formulas of approximate bias, variance and mean square error for the ordinary least square estimator and approximate variance for the weighted least square estimator after linearization of least square estimators. Also we compare their magnitudes each other numerically through a simulation study. We consider a three years data of Korean Welfare Panel Study as a finite population and take household income as a dependent variable and choose 7 exploratory variables related household as independent variables in panel regression model. Then we calculate approximate bias, variance, mean square error for the ordinary least square estimator and approximate variance for the weighted least square estimator based on several sample sizes from 50 to 1,000 by 50. Through the simulation study we found some tendencies as follows. First, the mean square error of the ordinary least square estimator is getting larger than the variance of the weighted least square estimator as sample sizes increase. Next, the magnitude of mean square error of the ordinary least square estimator is depending on the magnitude of the bias of the estimator, which is large when the bias is large. Finally, with regard to approximate variance, variances of the ordinary least square estimator are smaller than those of the weighted least square estimator in many cases in the simulation.