• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.255-264
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• 2008

It is common in practice to use mean squared error(MSE) for prediction. Recently, Park and Shin (2005) and Jones et al. (2007) studied prediction based on mean squared relative error(MSRE). We proposed a new nonparametric way of prediction based on MSRE substituting Jones et al. (2007) and provided a small simulation study which highly supports the proposed method.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.515-525
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• 2010

We investigated design-based properties of the ordinary least square estimator(OLSE) and the weighted least square estimator(WLSE) in a panel regression model. Given a complex data we derive the magnitude of the design-based bias of two estimators and show that the bias of WLSE is smaller than that of OLSE. We also conducted a simulation study using Korean welfare panel data in order to compare design-based properties of two estimators numerically. In the study we found the followings. First, the relative bias of OLSE is nearly two times larger than that of WLSE and the bias ratio of OLSE is greater than that of WLSE. Also the relative bias of OLSE remains steady but that of WLSE becomes smaller as the sample size increases. Next, both the variance and mean square error(MSE) of two estimators decrease when the sample size increases. Also there is a tendency that the proportion of squared bias in MSE of OLSE increases as the sample size increase, but that of WLSE decreases. Finally, the variance of OLSE is smaller than that of WLSE in almost all cases and the MSE of OLSE is smaller in many cases. However, the number of cases of larger MSE of OLSE increases when the sample size increases.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.6
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• pp.70-75
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• 2000

This paper examines the performance of adaptive filtering algorithms in relation to the asymptotic relative efficiency (ARE) of estimators. The adaptive filtering algorithms are Hybrid II and modified zero forcing (MZF) algorithms. The Hybrid II and MZF algorithms are simplified forms of the LMS algorithm, which use the polarity of the input signal, and polarities of the error and input signals, respectively. The ARE of estimators for each algorithm is analyzed under the condition of the same convergence speed. Computer simulations for adaptive equalization are performed to check the validity of the theory. The explicit expressions for the ARE values of the Hybrid II and MZF algorithms are derived, and its results have similar values to the results of computer simulation. It also revealed that the ARE values depend on the correlation coefficients between input signal and error signal.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.349-356
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• 2009

In this study, we suggest the estimation method of the relative risk for the unemployment statistics of a small area such as si, gun, gu in Korea. The considered method are the usual pooled estimator, weighted estimator with the inverse of log-variance as weights, and the Jackknife estimator. And we compare with the efficiency of the three estimators by estimating the bias and mean square errors using real data from the 2002 Economically Active Population Survey of Gyeonggi-do. We compute the unemployed rate of male and female in small areas, and then estimate the common relative risk for the unemployed rate between male and female. Also, the stability and reliability of the three estimators for the common relative risk was evaluated using the RB(relative bias) and the RRMSE(relative root mean square error) of these estimators. Finally, the Jackknife estimator turned out to be much more efficient than the other estimators.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.1-14
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• 2003

In this study, we suggest the method of small area estimation based on the Economically Active Population Survey (EAPS) data in producing unemployment statistics for the local self-government areas (LSGAs) within large areas. The small area estimators considered are design-based indirect estimators such as the synthetic and composite estimators. The jackknife mean square error was used as a measure of accuracy of such small area estimators. The total unemployed and jackknife mean square errors of the 10 LSGAs within the large area of ChoongBuk region are derived from the estimation procedure suggested in this study, using EAPS data of December 2000. The reliability of small area estimators was assessed using the relative bias values and relative root mean square errors of these estimators. We find that under the current Korean EAPS system, the composite estimator turns out to be much more stable than other estimators.

• The Korean Journal of Applied Statistics
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• v.12 no.1
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• pp.109-124
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• 1999

일반적으로 오차항이 자기상관되어 있는 선형회귀 모형에서는 회귀계수에 대한 보통최소제곱추정량이 효율적이지 못 하다고 알려져 있다. 그러나 이러한 일반화선형회귀모형에서 독립변수의 형태에 따라서는 OLSE의 사용 가능성을 제시하는 모형이 있다. 본 연구에서는 오차항이 일차 이동평균 과정을 따르는 선형회귀모형에서 여러 추정량들 (GLSE, APX, MAPX)에 대한 OLSE의 상대효율함수를 유도하고 비교 분석하고자 한다. 특히 소표본에서 정확한 상대효율값을 구하여 OLSE의 효율성이 크게 떨어지지 않거나 효율성이 나은 회귀모형들을 제시한다.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1B
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• pp.1-7
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• 2012

Quasi-two dimensional numerical model (GSTARS) was applied to determine the optimal sediment discharge formula for simulating the sedimentologic characteristics of Hyeongsan river. The field measurements have been conducted to obtain the data, such as sediment discharge, bed material, and channel geometry, for model calibration and verification. The sediment discharge formulas, which have been generally used, have been assessed according to the average error, relative error, RMSE, RRMSE, discrepancy ratio and Nash-Sutcliffe efficiency coefficient for bed changes along the thalweg. From the results, Laursen formula(1958) shows the best performance to simulate the long-term bed change of Hyeongsan river.

• Journal of Korea Water Resources Association
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• v.56 no.8
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• pp.509-520
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• 2023

Various drought indices are widely used for assessing drought conditions which are affected by many factors such as precipitation, soil moisture, and runoff. The values of drought indices varies depending on hydro-meteorological data and calculation formulas, and the judgment of the drought condition may also vary. This study selected four calculation components such as precipitation data length, accumulation period, probability distribution function, and parameter estimation method as the sources of uncertainty in the calculation of standardized precipitation index (SPI), and evaluated their contributions to the uncertainty using root mean square error (RMSE) and linear mixed model (LMM). The RMSE estimated the overall errors in the SPI calculation, and the LMM was used to quantify the uncertainty contribution of each factor. The results showed that as the accumulation period increased and the data period extended, the RMSEs decreased. The comparison of relative uncertainty using LMM indicated that the sample size had the greatest impact on the SPI calculation. In addition, as sample size increased, the relative uncertainty related to the sample size used for SPI calculation decreased and the relative uncertainty associated with accumulation period and parameter estimation increased. In conclusion, to reduce the uncertainty in the SPI calculation, it is essential to collect long-term data first, followed by the appropriate selection of probability distribution models and parameter estimation methods that represent well the data characteristics.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.1
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• pp.153-160
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• 2020

The kinetic energy of the rain drops was predicted in a relation between the rain rate and rain quantity, derived directly from the rain drop size distribution (DSD), which had been measured by a disdrometer located in the eastern state of Alagoas-Brazil. The equation in the form of exponential form suppressed the effects of large drops at low rainfall intensity observed at the beginning and end of the rainfall. The kinetic energy of the raindrop was underestimated in almost rain intensity ranges and was considered acceptable by the performance indicators such as coefficient of determination, average absolute error, percent relative error, mean absolute error, root mean square error, Willmott's concordance index and confidence index.