• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.109-112
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• 2005

The robust quasi-likelihood (RQL) proposed by Cantoni & Ronchetti (2001) is a robust version of quasi-likelihood. They adopted Huber function to increase the resistance of the RQL estimator to the outliers. They considered the Huber function only of symmetric type. We extend the class of Huber function to include asymmetric types, and derived a method to find the optimal asymmetric one.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.543-549
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• 2008

Inspired by using a robust loss function in the support vector machine regression to control training error and the idea of robust template matching with M-estimator, Chen (2004) applies M-estimator techniques to gaussian radial basis functions and form a new class of robust kernels for the support vector machines. We are specially interested in the shape of the Huber's M-estimator in this context and propose a way to find the shape parameter of the Huber's M-estimating function. For simplicity, only the two-class classification problem is considered.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.181-188
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• 2000

The shape of an M-estimation function is generally determined in the sense of either/both maximizing efficiency of an M-estimator at the model or/and bounding the influence function of an M-estimator. We propose an empirical method of choosing a value of the bending constant in Huber's ${\psi}-function$, which is the most widely used M-estimation function when estimating the location parameter.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.291-308
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• 2024

The current article discusses ratio type exponential estimators for estimating the mean of a finite population in sample surveys. The estimators uses robust regression's Huber M-estimation function, and their bias as well as mean squared error expressions are derived. It was campared with Kadilar, Candan, and Cingi (Hacet J Math Stat, 36, 181-188, 2007) estimators. The circumstances under which the suggested estimators perform better than competing estimators are discussed. Five different population datasets with a well recognized outlier have been widely used in numerical and simulation-based research. These thorough studies seek to provide strong proof to back up our claims by carefully assessing and validating the theoretical results reported in our study. The estimators that have been proposed are intended to significantly improve both the efficiency and accuracy of estimating the mean of a finite population. As a result, the results that are obtained from statistical analyses will be more reliable and precise.

• The Korean Journal of Applied Statistics
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• v.14 no.2
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• pp.357-367
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• 2001

Huber의 M-추정함수의 형태는 조율상수가 주어질 때 비로소 그 형태가 결정된다. 조율상수를 커널밀도함수추정량의 평활계수를 이용하여 구하여 보았고, 모의실험을 통해 기존에 상요되는 조율상수들과 그 성능을 비교하여 보았다. 그 결과 새로운 방법에 의해 구해진 조율상수가 기존의 조율상수를 사용하는 경우 보다 모의실험을 통해 얻은 추정치의 분산이 작게되는 경우가 있음을 알았다.

• The Journal of Korea Robotics Society
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• v.18 no.3
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• pp.330-336
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• 2023

In this paper, a novel line-based simultaneous localization and mapping (SLAM) using a loss function of vanishing point measurements is proposed. In general, the Huber norm is used as a loss function for point and line features in feature-based SLAM. The proposed loss function of vanishing point measurements is based on the unit sphere model. Because the point and line feature measurements define the reprojection error in the image plane as a residual, linear loss functions such as the Huber norm is used. However, the typical loss functions are not suitable for vanishing point measurements with unbounded problems. To tackle this problem, we propose a loss function for vanishing point measurements. The proposed loss function is based on unit sphere model. Finally, we prove the validity of the loss function for vanishing point through experiments on a public dataset.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.5
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• pp.39-48
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• 2009

Many super-resolution reconstruction algorithms have been proposed since it was the first proposed in 1984. The spatial domain approach of the super-resolution reconstruction methods is accomplished by mapping the low resolution image pixels into the high resolution image pixels. Generally, a super-resolution reconstruction algorithm by using the spatial domain approach has the noise problem because the low resolution images have different noise component, different PSF, and distortion, etc. In this paper, we proposed the new super-resolution reconstruction method that uses the L1 norm to minimize noise source and also uses the Huber norm to preserve edges of image. The proposed algorithm obtained the higher image quality of the result high resolution image comparing with other algorithms by experiment.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.124-129
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• 2007

For seismic imaging and inversion, the inverted image depends on how we define the objective function. ${\ell}^1$-norm is more robust than ${\ell}^2$-norm. However, it is difficult to apply the Newton-type algorithm directly because the partial derivative for ${\ell^1$-norm has a singularity. In our paper, to overcome the difficulties of singularities, Huber function given by hybrid ${\ell}^1/{\ell}^2$-norm is used. We tested the robustness of our new object function with several noisy data set. Numerical results show that the new objective function is more robust to band limited spiky noise than the conventional object function.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.93-100
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• 2003

It is necessary to check the curvature of selected covariates in regression diagnostics. There are various graphical methods using residual plots based on least squares fitting. The sensitivity of LS fitting to outliers can distort their residuals, making the identification of the unknown function difficult to impossible. In this paper, we compare combining conditional expectation and residual plots(CERES Plots) between least square fit and robust fits using Huber M-estimator. Robust CERES will be far less distorted than their LS counterparts in the presence of outliers and hence, will be more useful in identifying the unknown function.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.129-134
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• 2004

In this study, we investigate the effects of the weight function in the bounded influence regression quantile (BIRQ) estimator for the AR(1) model with additive outliers. In order to down-weight the outliers of X-axis, the Mallows' (1973) weight function has been commonly used in the BIRQ estimator. However, in our Monte Carlo study, the BIRQ estimator using the Tukey's bisquare weight function shows less MSE and bias than that of using the Mallows' weight function or Huber's weight function.