• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.501-512
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• 1997

In multiple linear regression model we have presupposed assumptions (independence normality variance homogeneity and so on) on error term. When case weights are given because of variance heterogeneity we can estimate efficiently regression parameter using weighted least squares estimator. Unfortunately this estimator is sen-sitive to outliers like ordinary least squares estimator. Thus in this paper we proposed some statistics for detection of outliers in weighted least squares regression.

• Journal of the Korean Statistical Society
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• 제8권1호
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• pp.23-36
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• 1979

In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

• 전기학회논문지
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• 제65권9호
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• pp.1541-1550
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• 2016

In this paper, we introduce a novel learning methodology of fuzzy clustering-based neural network pattern classifier. Fuzzy clustering-based neural network pattern classifier depicts the patterns of given classes using fuzzy rules and categorizes the patterns on unseen data through fuzzy rules. Least squares estimator(LSE) or weighted least squares estimator(WLSE) is typically used in order to estimate the coefficients of polynomial function, but this study proposes a novel coefficient estimate method which includes advantages of the existing methods. The premise part of fuzzy rule depicts input space as "If" clause of fuzzy rule through fuzzy c-means(FCM) clustering, while the consequent part of fuzzy rule denotes output space through polynomial function such as linear, quadratic and their coefficients are estimated by the proposed local least squares estimator(LLSE)-based learning. In order to evaluate the performance of the proposed pattern classifier, the variety of machine learning data sets are exploited in experiments and through the comparative analysis of performance, it provides that the proposed LLSE-based learning method is preferable when compared with the other learning methods conventionally used in previous literature.

• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.21-32
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• 1997

Robust regression based on M-estimator reduces and/or bounds the influence of outliers in the y-direction only. Therefore, when several influential observations exist, diagnostics in the robust regression is required in order to detect them. In this paper, we propose influence diagnostics in the robust regression based on M-estimator and its one-step version. Noting that M-estimator can be obtained through iterative weighted least squares regression by using internal weights, we apply the weighted least squares (WLS) regression diagnostics to robust regression.

• 대한전기학회논문지
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• 제41권9호
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• pp.1021-1030
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• 1992

When using a least squares estimator with exponential forgetting factor to identify continuous-time deterministic system, the problem of determining minimum eigenvalue is described in this paper. It is well known fact that the convergence rate of parameter estimates relies on various factors consisting of the estimator and especially, theirproperties can be directly affected by all eigenvalues in the parameter error differential equation. Fortunately, there exists only one adjusting eigenvalue in the given estimator and then, the parameter convergence rates depend on this minimum eigenvalue. In this note, a new result to determine the minimum eigenvalue is proposed. Under the assumption that the input has as many spectral lines as the number of parameter estimates, it can be proven that the minimum eigenvalue converges to a constant value, which is a function of the forgetting factor and the parameter estimates number.

• 응용통계연구
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• 제19권1호
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• pp.97-110
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• 2006

대부분의 자료는 여러가지 원인으로 인한 특이치로 오염되어 있으며, 이러한 상황에서 신뢰성 있는 추정량을 얻어내고 이에 대한 통계적 추론을 시행하는 것은 중요한 문제이다. 그러나 이제까지 제안된 로버스트 회귀추정량들은 계산상의 어려움과 정규오차모형에서 최소제곱추정량에 비하여 떨어지는 효율성때문에 통계적 추론의 정확성을 확신할 수 없었다. 최근 제안된 Lee(2004)의 가중자기조율회귀추정량(weighted self-tuning estimator, WSTE)은 다른 로버스트 회귀추정량에 비하여 정확한 계산과정과 그에 따른 추정량의 점근적 정규성 및 고붕괴점을 갖는다. 그러나 통계적 추론을 위하여 이제까지 널리 사용해왔던 로버스트 추정량에 기반한 가중최소제곱추정방법(weighted least squares estimator)은 WSTE에서조차 정규오차모형하에서 최소제곱추정량과 동일한 수준의 효율성을 제공해주지 는 못한다. 본 논문에서는 WSTE에 기반한 또다른 통계적 추론 방법을 제안하고, 이 방법을 사용함으로써 정규오차모형 및 대표본에서 보다 정확한 결과를 얻을 수 있음을 몬테칼로 모의실험을 통해 제시하였다.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.639-647
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• 2002

Efforts to obtain more power for unit root tests have continued. Pantula at el.(1994) compared empirical powers of several unit root test statistics and addressed that the weighted symmetric estimator(WSE) and the unconditional maximum likelihood estimator(UMLE) are the best among them. One can easily see that the powers of these two statistics are almost the same. In this paper we explain a connection between WSE and UMLE and suggest a unit root test statistic which may explain the connection between them.

• Communications for Statistical Applications and Methods
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• 제4권3호
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• pp.903-909
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• 1997

The ordinary least squares estimator and the corresponding pivotal statistics have been widely used for the unit test. Recently several test criteria based on maximum likelihood estimators and weighted symmetric estimator have been proposed for testing the unit root hypothesis in the autoregressive processes. Pantula at el. (1994) showed that the weighted symmetric estimator has good power properties. In this article we use an adjusted estimator for mean in the model when we use weighted symmetric estimator. A simulation study shows that for the small samples, this new test criterion has better power properties than the weighted symmetric estimator.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 추계학술대회 논문집 전기물성,응용부문
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• pp.279-282
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• 2003

In this paper, we propose a new high resolution frequency estimator for real sinusoids by using short time data and the AWLS/MFT (Adaptive Weighted Least Squares/ Modulation Function Technique) algorithm. Monte-Carlo simulations verify better performances of the proposed frequency estimator and demonstrate that the proposed AWLS sinusoidal estimator is a high resolution estimator.