• 대한의용생체공학회:의공학회지
• /
• 제19권2호
• /
• pp.133-142
• /
• 1998

Bayesian SPECT 영상재구성에 있어서 정교한 형태의 사전정보를 사용할 경우 bias 및 variance와 같은 통계적 차원에서의 정량적 성능을 향상시킬 수 있다. 특히, "thin plate" 와 같은 고차의 smoothing 사전정보는 "membrane"과 같은 일반적인 다른 사전 정보에 비해 bias를 개선시키는 것으로 알려져 있다. 그러나, 이와 같은 장점은 영상재구성 알고리즘에 내재하는 hyperparameters의 값을 최적으로 선택하였을 경우에만 적용된다. 본 연구에서는 thin plate와 membrane의 두가지 대표적인 사전정보를 포함하는 영상재구성 알고리즘의 정량적 성능에 대해 집중 고찰한다. 즉, 알고리즘에 내재하는 hyperparameters 가 통계적 차원에서 bias와 variance에 어떠한 영향을 미치는지 관찰한다. 실험에서 Monte Carlo noise trials를 사용하여 bias와 variance를 계산하며, 각 결과를 ML-EM 및 filtered backprojection으로부터 얻어진 bias 및 variance와 비교한다. 결론적으로 thin plate와 같은 고차의 사전정보는 hyperparameters의 선택에 민감하지 않으며, hyperparameters 값의 전 범위에 걸쳐 bias를 개선시킴을 보인다. 걸쳐 bias를 개선시킴을 보인다.

• 대한산업공학회지
• /
• 제38권1호
• /
• pp.25-30
• /
• 2012

Desirability approaches have been proposed to find an optimum of multiple response problem. The existing desirability approaches use either of mean or min of individual desirability in aggregation of multiple responses. However, in order to find an optimum having high mean and low dispersion among individual desirability, the dispersion needs to be simultaneously considered with its mean. This study proposes bias and variance (BV) method which aggregates bias (ideal target-mean) and variance of individual desirability in multiple response optimization. The proposed BV method was applied to an example to evaluate its usefulness by comparing with existing methods. Evaluation results showed that the solution of BV method was a fairly good compared with DS (Derringer and Suich, 1980) and KL (Kim and Lin, 2000) methods. The BV method can be utilized to multiple response surface problems when decision makers want to find an optimum having high mean and low variance among responses.

• Communications for Statistical Applications and Methods
• /
• 제19권1호
• /
• pp.23-32
• /
• 2012

본 논문은 유한모집단에서 회귀계수추정량의 근사편향과 근사분산을 다루고 있다. 유한모집단에서 고정크기 포함확률비례표본을 추출하고 이 표본에서 조사된 데이터에 기초하여 회귀계수를 일반최소제곱추정량과 가중최소제곱추정량으로 추정할 때 두 추정량의 편향, 분산 그리고 평균제곱오차의 근사식을 유도하였다. 그리고 두 추정량의 효율을 비교하기 위하여 두 추정량의 분산을 비교하는 필요충분조건을 제시하였다. 또한 수치적인 비교를 위하여 간단한 예제를 소개하였다.

• Journal of the Korean Statistical Society
• /
• 제12권2호
• /
• pp.81-90
• /
• 1983

The least squares estimator of disturbance variance in a regression model is biased under a serial correlation. Under the assumption of an AR(I), Theil(1971) crudely related the bias with the autocorrelation of the disturbances and the autocorrelation of the explanatory variable for a simple regression. In this paper we derive a relation which relates the bias with the autocorrelation of disturbances and the autocorrelation of explanatory variables for a multiple regression with improved precision.

• 대한산업공학회지
• /
• 제28권1호
• /
• pp.112-127
• /
• 2002

A useful pattern is a pattern that contributes much to learning. For a classification problem those patterns near the class boundary surfaces carry more information to the classifier. For a regression problem the ones near the estimated surface carry more information. In both cases, the usefulness is defined only for those patterns either without error or with negligible error. Using only the useful patterns gives several benefits. First, computational complexity in memory and time for learning is decreased. Second, overfitting is avoided even when the learner is over-sized. Third, learning results in more stable learners. In this paper, we propose a pattern 'utility index' that measures the utility of an individual pattern. The utility index is based on the bias and variance of a pattern trained by a network ensemble. In classification, the pattern with a low bias and a high variance gets a high score. In regression, on the other hand, the one with a low bias and a low variance gets a high score. Based on the distribution of the utility index, the original training set is divided into a high-score group and a low-score group. Only the high-score group is then used for training. The proposed method is tested on synthetic and real-world benchmark datasets. The proposed approach gives a better or at least similar performance.

• 통합자연과학논문집
• /
• 제5권4호
• /
• 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.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2002년도 춘계 학술발표회 논문집
• /
• pp.183-188
• /
• 2002

Multiple imputation, proposed by Rubin, is a procedure for handling missing data. One of the attractive parts of multiple imputation is the simplicity of the variance estimation formula. Because of the simplicity, it has been often abused and misused beyond its original prescription. This paper provides the bias of the multiple imputation variance estimator for a linear point estimator and discusses when the bias can be safely neglected.

• Journal of the Korean Statistical Society
• /
• 제24권2호
• /
• pp.507-518
• /
• 1995

The ordinary least squares based estiamte $S^2$ of the disturbance variance is considered in the linear regression model when the disturbances follow the first-order moving-average process. It is shown that $S^2$ is weakly consistent estimate for the disturbance varaince without any restriction on the regressor matrix X. Also, simple exact bounds on the relative bias of $S^2$ are given in finite sample sizes.

• 한국경영과학회:학술대회논문집
• /
• 대한산업공학회/한국경영과학회 2004년도 춘계공동학술대회 논문집
• /
• pp.294-297
• /
• 2004

Mean squared error (MSE) is an effective criterion to combine the mean and the standard deviation responses in dual response surface optimization. The bias and variance components of MSE need to be weighted properly in the given problem situation. This paper proposes a systematic method to determine the relative weights of bias and variance in accordance with a decision maker's prior and posterior preference structure.

• 한국경영과학회지
• /
• 제21권3호
• /
• pp.159-174
• /
• 1996

Facing decision-making tasks, managers frequently make judgments, However, since managers are human beings, the fficiency of their judgments is limited. Two major sources of inefficiency in their judgments have been recognized : one is systematic deviations from normatively preferred decisions, so called bias or incorrect intuition, and the other is inconsistency in their judgments, i. e. erratic decision making variance. Rather than bias, variance is really expensive or damaging. Thus, if the inconsistency inmanagers judgments is removed, performance could be by far improved by virtue of the reduced random variance. One of the approaches to improve managerial judgment is to simply bring managers together by effectively moderating the random variance due to inconsistency. Focusing on combining judgments, this paper addresses many relevant issues such as why combining and how to combine judgments, and suggests methods and models to effectively aggregate subjective judgments, We conduct an experiment to validata the effectiveness of combining jugements over individual judgments. Various combining schemes are also evaluated in terms of their prective accuracy. Among them, mean bias based wighting scheme turns out the best. However, when available information is not enough to estimate the expertise of judges, simple and robust equal weighting might be more efficient and productive. This urges an imperative future research on the issue of how many and which ones to combine from a large set of experts.