• Journal of the Korean Statistical Society
• /
• v.27 no.4
• /
• pp.459-469
• /
• 1998

Balanced half sample method is a simple variance estimation method for complex sampling designs. Since it is simple and flexible, it has been widely used in large scale sample surveys. However, the usual BHS method overestimate the true variance in without replacement sampling and two-stage cluster sampling. Focusing on this point , we proposed an unbiased BHS variance estimator in a stratified two-stage cluster sampling and then described an implementation method of the proposed estimator. Finally, partially BHS design is explained as a tool of reducing the number of replications of the proposed estimator.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.16 no.1
• /
• pp.59-67
• /
• 1991

The hazard estimator is proposed for estimating system failure probability of a general network where all minimal cut sets are given. Theoretical variance of the hazard estimator is derived in a bridge system. It is demonstrated that variance of the hazard estimator is much smaller than that of the raw simulation estimator particularly for small arc failure probability.

• Communications for Statistical Applications and Methods
• /
• v.19 no.3
• /
• pp.333-344
• /
• 2012

We consider some statistical properties of the first order difference-based error variance estimator in nonparametric regression models with a single outlier. So far under an outlier(s) such difference-based estimators has been rarely discussed. We propose the first order difference-based estimator using the leave-one-out method to detect a single outlier and simulate the outlier detection in a nonparametric regression model with the single outlier. Moreover, the outlier detection works well. The results are promising even in nonparametric regression models with many outliers using some difference based estimators.

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

• Proceedings of the Korean Association for Survey Research Conference
• /
• 2001.11a
• /
• pp.77-85
• /
• 2001

In this paper we study the calibration estimator and its variance estimator for the population total using a bootstrap method according to the levels of an auxiliary information having strong correlation with an interested variable in nonresponse situation. At this point, we find tire calibration estimator in case of auxiliary information for population and sample, and then we drive the bootstrap variance estimator of it. By simulation study we compare the efficiencies with the Taylor and Jackknife variance estimators.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.1
• /
• pp.61-71
• /
• 1993

We focus on a way of combining the Monte Calro methods of antithetic variates and control variates to reduce the variance of the estimator of the mean response in a simulation experiment. Combined Method applies antithetic variates (partially) for driving approiate stochastic model components to reduce the vaiance of estimator and utilizes the correlations between the response and control variates. We obtain the variance of the estimator for the response analytically and compare Combined Method with control variates method. We explore the efficiency of this method in reducing the variance of the estimator through the port operations model. Combined Method shows a better performance in reducing the variance of estimator than methods of antithetic variates and control variates in the range from 6% to 8%. The marginal efficiency gain of this method is modest for the example considered. When the effective set of control variates is small, the marginal efficiency gain may increase. Though these results are from the limited experiments, Combined Method could profitably be applied to large-scale simulation models.

• Proceedings of the Korean Association for Survey Research Conference
• /
• 2001.04a
• /
• pp.59-71
• /
• 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
• /
• v.2 no.1
• /
• pp.59-71
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.79-88
• /
• 2003

In this paper, we study the efficiency of the stratified estimator in related with the variance lower bound of Horvitz-Thompson estimator subject to the superpopulation model. Especially, we compare the variance lower bound of optimum allocation with that of power allocation subject to Dalenius-Hedges stratification.

• Journal of Integrative Natural Science
• /
• v.5 no.4
• /
• pp.241-245
• /
• 2012

Categorical data collected based on complex sample design is not proper for the standard Pearson multinomial-based chi-squared test because the observations are not independent and identically distributed. This study investigates effects of bias of point estimator of population proportion and its variance estimator to the standard Pearson chi-squared test statistics when the sample is collected based on complex sampling scheme. This study examines the effect under two population homogeneity test. The standard Pearson test statistic can be partitioned into two parts; the first part is the weighted sum of ${\chi}^2_1$ with eigenvalues of design matrix as their weights, and the additional second part which is added due to the biases of the point estimator and its variance estimator. Our empirical analysis shows that even though the bias of point estimator is small, Pearson test statistic is very much inflated due to underestimate the variance of point estimator. In the connection of design-based variance estimator and its design matrix, the bigger the average of eigenvalues of design matrix is, the larger relative size of which the first component part to Pearson test statistic is taking.