• Title/Summary/Keyword: 평균제곱

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Design-Based Properties of Least Square Estimators of Panel Regression Coefficients Based on Complex Panel Data (복합패널 데이터에 기초한 최소제곱 패널회귀추정량의 설계기반 성질)

  • Kim, Kyu-Seong
    • 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.

A New Nonparametric Method for Prediction Based on Mean Squared Relative Errors (평균제곱상대오차에 기반한 비모수적 예측)

  • Jeong, Seok-Oh;Shin, Key-Il
    • 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.

Numerical Integration-based Performance Analysis of Amplitude-Comparison Monopulse System (진폭비교 모노펄스시스템의 수치적분 기반 성능분석)

  • Ham, Hyeong-Woo;Lim, Hee-Yun;Lee, Joon-Ho
    • Journal of Digital Convergence
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    • v.19 no.12
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    • pp.339-345
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    • 2021
  • In this paper, estimation angle performance analysis of amplitude-comparison monopulse radar under additive noise effect is dealt with. When uncorrelated white noises are added to the squinted beams, the angle estimation performance is analyzed through the mean square error(MSE). The numerical integration-based mean square error result completely overlaps the Monte Carlo-based mean square error result, which corresponds to 99.8% of the Monte Carlo-based mean square error result. In addition, the mean square error analysis method based on numerical integration has a much faster operation time than the mean square error method based on Monte Carlo. the angle estimation performance of the amplitude comparison monopulse radar can be efficiently analyzed in various noise environments through the proposed numerical integration-based mean square error method.

Design-based Properties of Least Square Estimators in Panel Regression Model (패널회귀모형에서 회귀계수 추정량의 설계기반 성질)

  • Kim, Kyu-Seong
    • 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.

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Estimation of nonlinear GARCH-M model (비선형 평균 일반화 이분산 자기회귀모형의 추정)

  • Shim, Joo-Yong;Lee, Jang-Taek
    • Journal of the Korean Data and Information Science Society
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    • v.21 no.5
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    • pp.831-839
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    • 2010
  • Least squares support vector machine (LS-SVM) is a kernel trick gaining a lot of popularities in the regression and classification problems. We use LS-SVM to propose a iterative algorithm for a nonlinear generalized autoregressive conditional heteroscedasticity model in the mean (GARCH-M) model to estimate the mean and the conditional volatility of stock market returns. The proposed method combines a weighted LS-SVM for the mean and unweighted LS-SVM for the conditional volatility. In this paper, we show that nonlinear GARCH-M models have a higher performance than the linear GARCH model and the linear GARCH-M model via real data estimations.

The Comparison of the Performance for LMS Algorithm Family Using Asymptotic Relative Efficiency (점근상대효율을 이용한 최소평균제곱 계열 적응여파기의 성능 비교)

  • Sohn, Won
    • 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.

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A Weighted Mean Squared Error Approach to Multiple Response Surface Optimization (다중반응표면 최적화를 위한 가중평균제곱오차)

  • Jeong, In-Jun;Cho, Hyun-Woo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.14 no.2
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    • pp.625-633
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    • 2013
  • Multiple response surface optimization (MRSO) aims at finding a setting of input variables which simultaneously optimizes multiple responses. The minimization of mean squared error (MSE), which consists of the squared bias and variance terms, is an effective way to consider the location and dispersion effects of the responses in MRSO. This approach basically assumes that both the terms have an equal weight. However, they need to be weighted differently depending on a problem situation, for example, in case that they are not of the same importance. This paper proposes to use the weighted MSE (WMSE) criterion instead of the MSE criterion in MRSO to consider an unequal weight situation.

Weighting Effect on the Weighted Mean in Finite Population (유한모집단에서 가중평균에 포함된 가중치의 효과)

  • Kim, Kyu-Seong
    • Survey Research
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    • v.7 no.2
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    • pp.53-69
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    • 2006
  • Weights can be made and imposed in both sample design stage and analysis stage in a sample survey. While in design stage weights are related with sample data acquisition quantities such as sample selection probability and response rate, in analysis stage weights are connected with external quantities, for instance population quantities and some auxiliary information. The final weight is the product of all weights in both stage. In the present paper, we focus on the weight in analysis stage and investigate the effect of such weights imposed on the weighted mean when estimating the population mean. We consider a finite population with a pair of fixed survey value and weight in each unit, and suppose equal selection probability designs. Under the condition we derive the formulas of the bias as well as mean square error of the weighted mean and show that the weighted mean is biased and the direction and amount of the bias can be explained by the correlation between survey variate and weight: if the correlation coefficient is positive, then the weighted mein over-estimates the population mean, on the other hand, if negative, then under-estimates. Also the magnitude of bias is getting larger when the correlation coefficient is getting greater. In addition to theoretical derivation about the weighted mean, we conduct a simulation study to show quantities of the bias and mean square errors numerically. In the simulation, nine weights having correlation coefficient with survey variate from -0.2 to 0.6 are generated and four sample sizes from 100 to 400 are considered and then biases and mean square errors are calculated in each case. As a result, in the case or 400 sample size and 0.55 correlation coefficient, the amount or squared bias of the weighted mean occupies up to 82% among mean square error, which says the weighted mean might be biased very seriously in some cases.

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A Robust Design of Response Surface Methods (반응표면방법론에서의 강건한 실험계획)

  • 임용빈;오만숙
    • The Korean Journal of Applied Statistics
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    • v.15 no.2
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    • pp.395-403
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    • 2002
  • In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

Analysis of Distance Measurement Accuracy in Aerial and Satellite Image Photogrammetry (항공사진측량과 위성영상측량에서 거리측정 정확도 연구)

  • Kim, Hyung-Moo;Tcha, Dek-Kie;Nam, Guon-Mo;Yang, Chul-Soo
    • Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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    • 2010.04a
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    • pp.253-255
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    • 2010
  • Needs to study on distance measurement accuracy in aerial and satellite photogrammetry are rapidly increased. However, conventional studies show some confused definitions between measurement accuracy and measurement precision as well as standard deviation(STDEV) and root mean square error(RMSE or RMSD). So, Finite definitions of measurement accuracy and measurement precision as well as STDEV and RMSD are addressed in this paper. Experiment result show using correct definitions improve the distance measurement accuracy in aerial and satellite photogrammetry rapidly, but not the distance measurement accuracy in aerial and satellite photogrammetry.

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