• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.1033-1041
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• 2013

In this paper, we investigate several variance estimators for pps systematic sampling. Unfortunately, there is no unbiased variance estimators for a systematic sample because systematic sampling can be regarded as a random selection of one cluster. This study provides guidance on which variance estimator may be more appropriate than others in several circumstances. We judge the efficiency of variance estimators for systematic sampling based on of their relative biases and relative mean square error. Also, we investigate variance estimation problems for two-stage systematic sampling applied for the Food Raw Material Consumption Survey and the Establishment Labor Force Survey simulation study, in order to consider the popular two-stage pps systematic sample design for establishment and household survey in Korea.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1247-1253
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• 2008

In this paper, we propose a interval censored regression spline model with a variance function (non-constant variance that depends on a predictor). Simulation studies show our estimates from MCECM algorithm are consistent, but biased when the sample size is small because of boundary effects. Also, we examined how the distribution of $x_i$ affects the converging speed of these consistent estimates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1449-1454
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• 2009

The performance variation of a multibody system is affected by a variation of various design variables of the system. And the effects of design variable variations on the performance variation must be considered in design of a multibody system. Accordingly, a variation analysis of a multibody system needs to be conducted in design of a multibody system. For a variation analysis of a performance, population mean and variance which are called statistical parameters of design variables are needed. However, an evaluation of statistical parameters of design variables is impossible in many practical cases. Therefore, an estimation of statistical parameters of the performance based on sample mean and variance which are called statistic of design variables is needed. In this paper, the variation analysis method for a multibody system based on design variable samples was proposed. And, using the proposed method, a variation analysis of the vehicle ride comfort based on sample statistic of design variables was conducted.

• Journal of Korean Society for Quality Management
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• v.27 no.1
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• pp.46-58
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• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.

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

• Proceedings of the Korean Association for Survey Research Conference
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• 2002.11a
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• pp.255-274
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• 2002

We classify rotation sampling designs into two classes. The first class replaces sample units within the same rotation group while the second class replaces sample units between different rotation groups. The first class is specified by the three-way balanced design which is a multi-level version of previous balanced designs. We introduce an extended generalized composite estimator (EGCE) and derive its variance and mean squared error for each of the two classes of design, cooperating two types of correlations and three types of biases. Unbiased estimators are derived for difference between interview time biases, between recall time biases, and between rotation group biases. Using the variance and mean squared error, since any rotation design belongs to one of the two classes and the EGCE is a most general estimator for rotation design, we evaluate the efficiency of EGCE to simple weighted estimator and the effects of levels, design gaps, and rotation patterns on variance and mean squared error.

• Journal of Environmental Impact Assessment
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• v.24 no.6
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• pp.607-618
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• 2015

Five years have passed since the first set of environmental samples was taken in 2011 to represent various ecosystems which would help future generations lead back to the past environment. Those samples have been preserved cryogenically in the National Environmental Specimen Bank(NESB) at the National Institute of Environmental Research. Even though there is a strict regulation (SOP, standard operating procedure) that rules over the whole sampling procedure to ensure each sample to represent the sampling area, it has not been put to the test for the validation. The question needs to be answered to clear any doubts on the representativeness and the quality of the samples. In order to address the question and ensure the sampling practice set in the SOP, many steps to the measurement of the sample, that is, from sampling in the field and the chemical analysis in the lab are broken down to evaluate the uncertainty at each level. Of the 8 species currently taken for the cryogenic preservation in the NESB, pine tree samples from two different sites were selected for this study. Duplicate samples were taken from each site according to the sampling protocol followed by the duplicate analyses which were carried out for each discrete sample. The uncertainties were evaluated by Robust ANOVA; two levels of uncertainty, one is the uncertainty from the sampling practice, and the other from the analytical process, were then compiled to give the measurement uncertainty on a measured concentration of the measurand. As a result, it was confirmed that it is the sampling practice not the analytical process that accounts for the most of the measurement uncertainty. Based on the top-down approach for the measurement uncertainty, the efficient way to ensure the representativeness of the sample was to increase the quantity of each discrete sample for the making of a composite sample, than to increase the number of the discrete samples across the site. Furthermore, the cost-effective approach to enhance the confidence level on the measurement can be expected from the efforts to lower the sampling uncertainty, not the analytical uncertainty. To test the representativeness of a composite sample of a sampling area, the variance within the site should be less than the difference from duplicate sampling. For that, a criterion, ${i.e.s^2}_{geochem}$(across the site variance) <${s^2}_{samp}$(variance at the sampling location) was proposed. In light of the criterion, the two representative samples for the two study areas passed the requirement. In contrast, whenever the variance of among the sampling locations (i.e. across the site) is larger than the sampling variance, more sampling increments need to be added within the sampling area until the requirement for the representativeness is achieved.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.189-202
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• 1998

The goat of this paper is to study on variance estimation - Rice variance estimation, Gasser, Sroka and Jennen-Steinmetz's varince estimation - in smoothing goodness-of-fit tests. The comparisons of powers on test statistics are conducted by the change of variance, the number of oscillations, the amplitude of the alternative sample distribution.

• 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.

• Management & Information Systems Review
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• v.26
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• pp.293-309
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• 2008

This study examined the market efficiency of korea stock market by comparing variance ratios(VR) of stock groups which is sorted by market capitalization. We compute variance ratios of KOSPI large capitalization, midium capitalization, and small capitalization for 546 trading days from 2006/01/02 to 2008/04/15. For our study, we also use high frequency data that is; intra-day 1 minute data. The characteristics of variance ratios of stock groups by market capitalization as follows: From 1 to 5 minute interval, variance ratios of three stock group increase far from zero(0). The longer time interval, the more variance ratios decrease, but only large capitalization converge on around zero. This means that the market of large capitalization is more efficient compare to other stock groups. The entire sample period can be divided two sub-period because the impact of sub prime crisis arised from U.S.A. influences Korea stock market. Before sub prime crisis, the VRs of mid cap and small cap do not converge on around zero except large cap although the time interval is longer. After sub prime crisis, the VRs of three stock groups decrease when time interval is longer, but only large cap converge on around zero. We conclude that large cap is more efficient than other stock groups in Korea Stock Market.