• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.81-90
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• 2002

The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.

• Journal of the Korean Statistical Society
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• 제36권2호
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• pp.299-320
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• 2007

We introduce a high breakdown point estimator referred to as data partitioning robust regression estimator (DPR). Since the DPR is obtained by partitioning observations into a finite number of subsets, it has no computational problem unlike the previous robust regression estimators. Empirical and extensive simulation studies show that the DPR is superior to the previous robust estimators. This is much so in large samples.

• 대한수학회논문집
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• 제19권2호
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• pp.345-354
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• 2004

Boente and Fraiman [2] studied robust nonparametric estimators for regression or autoregression problems when the observations exhibit serial dependence. They established strong consistency of two families of M-type robust equivariant estimators for $\phi$-mixing processes. In this paper we extend their results to weaker $\alpha$$alpha$-mixing processes.

• 응용통계연구
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• 제29권3호
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• pp.471-485
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• 2016

회귀모형의 대표적인 추정법인 최소제곱법은 오차항의 분포가 정규분포를 따르고 이상치가 없는 상황에서는 최적이지만, 자료가 회귀모형의 가정을 만족하지 않을 경우 또는 이상치를 포함하는 경우와 같이 자료가 오염된 상황에서는 왜곡된 추정 결과를 준다. 따라서 이상치에 민감한 최소제곱법의 단점을 보완하기 위해 다양한 로버스트 추정방법이 제안되었다. 본 논문에서는 MLE를 기반으로 제안된 M 추정량, 순서형 통계량을 기반으로 제안된 L 추정량, 잔차의 순위를 기반으로 제안된 R 추정량 계열에서 높은 붕괴점 또는 높은 효율을 갖는 대표적인 추정량들을 다양한 모의실험을 통해 비교 연구하였다. 추정량의 성능을 비교하는데 효율성 뿐만 아니라 편의, 분산을 포함한 분포를 살펴보았다. 그 결과 실제 데이터 적용에는 MM 추정량과 GR 추정량이 좋은 성능을 가진 것으로 보였다.

• 한국컴퓨터정보학회논문지
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• 제10권2호
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• pp.21-30
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• 2005

강건 예측 기법은 오류 자료(outliers)를 제거하고 정상 자료(non-outliers)만으로 모델의 파라미터를 구하는 통계적인 방법으로 잘 알려져 있다 기존의 문헌에 소개된 많은 강건 예측 알고리즘들이 있으나 컴퓨터 비전 및 영상 처리 분야에서 가장 많이 사용되는 알고리즘은 M-estimators와 LMS(least-median of squares) 방법이다. 이 중 M-estimators는 어파인 모델(affine model)의 파라미터 측정에 있어 최적의 방법으로 잘 알려져 있다. 그러나 M-estimators는 통계적인 효율성이 높지만 초기화가 적절히 수행되지 않으면 오류 자료를 제거하는 데 문제점을 가진다 따라서 본 논문에서는 이런 문제점을 해결하기 위해 연속적인 시그모이드(sigmoid) 가중치 함수를 사용하여 오류 자료와 정상 자료를 효과적으로 분리하면서 어파인 모델의 파라미터를 효과적으로 측정하는 적응적인 M-estimators 강건 예측 알고리즘을 제안한다. 실험에서는 기존의 강건 예측 방법과 제안된 적응적 강건 예측 방법의 성능을 비교 및 분석하여 제안된 방법의 우수함을 보인다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2004년도 학술발표논문집
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• pp.205-210
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• 2004

A weighted self-tuning robust regression estimator (WSTE) has the high breakdown point for estimating regression parameters such as other well known high breakdown estimators. In this paper, we propose to obtain standard quantities like confidence intervals, and it is found to be superior to the other high breakdown regression estimators when a sample is contaminated

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.837-843
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• 2000

Kreiss and Franke(192) and Allen and Datta(1999) proposed bootstrapping the M-estimators in ARMA models. In this paper, we introduce the robust estimating function and investigate the bootstrap approximations of the M-estimators which are solutions of the estimating equations in TAR models. A number of simulation results are presented to estimate the sampling distribution of the M-estimators, and asymptotic validity of the bootstrap for the M-estimators is established.

• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.387-395
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• 2007

We propose a doubly robustified estimating function for the estimation of parameters in the context of ARCH models. We investigate asymptotic properties of estimators obtained as solutions of robust estimating equations. A simulation study shows that robust estimator from specified doubly robustified estimating equation provides better performance than conventional robust estimators especially under heavy-tailed distributions of innovation errors.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.551-561
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• 2001

This paper deals with the asymptotic properties for statistical inferences of the parameters in nonlinear regression models. As an optimal criterion for robust estimators of the regression parameters, the regression quantile method is proposed. This paper defines the regression quintile estimators in the nonlinear models and provides simple and practical sufficient conditions for the asymptotic normality of the proposed estimators when the parameter space is compact. The efficiency of the proposed estimator is especially well compared with least squares estimator, least absolute deviation estimator under asymmetric error distribution.

• ETRI Journal
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• 제44권6호
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• pp.915-924
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• 2022

In this paper, we present a two-stage scalable channel estimator (TSCE), a deep learning (DL)-based scalable, and robust channel estimator for wireless cellular networks, which is made up of two DL networks to efficiently support different resource allocation sizes and reference signal configurations. Both networks use the transformer, one of cutting-edge neural network architecture, as a backbone for accurate estimation. For computation-efficient global feature extractions, we propose using window and window averaging-based self-attentions. Our results show that TSCE learns wireless propagation channels correctly and outperforms both traditional estimators and baseline DL-based estimators. Additionally, scalability and robustness evaluations are performed, revealing that TSCE is more robust in various environments than the baseline DL-based estimators.