• Journal of Communications and Networks
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• 제9권2호
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• pp.185-191
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• 2007

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in signal processing. This class of process has no closed form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in S$\alpha$SG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm Kalman filtering algorithm based on least p-norm of innovation process with infinite variances, and a new robust multiuser detection method based on least p-norm Kalman filtering. The simulation experiments show that the proposed new algorithm is more robust than the conventional Kalman filtering multiuser detection algorithm.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• 응용통계연구
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• 제35권3호
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• pp.395-406
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• 2022

본 논문에서는 장기 종속 다변량 시계열 자료에 대한 이상점 탐지 기법을 연구한다. 기존 다변량 시계열 이상점 탐지 방법은 단기 종속 시계열 모형인 VARMA에 기반한 방법으로, 장기억성을 띈 다변량 시계열 자료에는 적합하지 않다. 자기회귀 모형을 통해서 장기 종속성, 즉 장기억성을 고려하기 위해서는 높은 차수의 모형이 필요하고, 이는 곧 추정의 불안성으로 이어지기에 장기억성을 효율적으로 다룰 수 없기 때문이다. 따라서, 본 논문은 이러한 문제를 보완하고자 VHAR 구조에 기반한 이상점 탐지 방법을 제시하고자 한다. 또한 더욱 정확한 추론을 위해서 로버스트한 방법을 이용하여 VHAR 계수를 추정하였고 이를 활용하여 이상점을 탐지하였다. 모의실험 결과 우리가 제안한 방법론이 기존 VARMA에 기반한 방법론보다 이상점 탐지에 더 효과적임을 살펴볼 수 있었다. 주가지수에 대한 실증자료 분석에서도 기존의 방법론은 탐지하지 못하는 추가 이상점을 찾음을 확인할 수 있었다.

• Communications for Statistical Applications and Methods
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• 제1권1호
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• pp.33-40
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• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• Communications for Statistical Applications and Methods
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• 제25권2호
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• pp.131-157
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• 2018

We propose a robust event date model to estimate the date of a target event by a combination of individual dates obtained from archaeological artifacts assumed to be contemporaneous. These dates are affected by errors of different types: laboratory and calibration curve errors, irreducible errors related to contaminations, and taphonomic disturbances, hence the possible presence of outliers. Modeling based on a hierarchical Bayesian statistical approach provides a simple way to automatically penalize outlying data without having to remove them from the dataset. Prior information on individual irreducible errors is introduced using a uniform shrinkage density with minimal assumptions about Bayesian parameters. We show that the event date model is more robust than models implemented in BCal or OxCal, although it generally yields less precise credibility intervals. The model is extended in the case of stratigraphic sequences that involve several events with temporal order constraints (relative dating), or with duration, hiatus constraints. Calculations are based on Markov chain Monte Carlo (MCMC) numerical techniques and can be performed using ChronoModel software which is freeware, open source and cross-platform. Features of the software are presented in Vibet et al. (ChronoModel v1.5 user's manual, 2016). We finally compare our prior on event dates implemented in the ChronoModel with the prior in BCal and OxCal which involves supplementary parameters defined as boundaries to phases or sequences.

• Communications for Statistical Applications and Methods
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• 제5권2호
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• pp.517-529
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• 1998

When the sample size is small the robust minimum Hellinger distance (HD) estimator can have substantially poor relative efficiency at the true model. Similarly, approximating the exact null distributions of the ordinary Hellinger distance tests with the limiting chi-square distributions can be quite inappropriate in small samples. To overcome these problems Harris and Basu (1994) and Basu et at. (1996) recommended using a modified HD called penalized Hellinger distance (PHD). Lindsay (1994) and Basu et al. (1997) showed that another density based distance, namely the negative exponential disparity (NED), is a major competitor to the Hellinger distance in producing an asymptotically fully efficient and robust estimator. In this paper we investigate the small sample performance of the estimates and tests based on the NED and penalized NED (PNED). Our results indicate that, in the settings considered here, the NED, unlike the HD, produces estimators that perform very well in small samples and penalizing the NED does not help. However, in testing of hypotheses, the deviance test based on a PNED appears to achieve the best small-sample level compared to tests based on the NED, HD and PHD.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.729-738
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• 2015

품질특성치의 중심과 산포를 하나의 통계량으로 관리하는 단일 관리도는 품질특성치가 정규분포를 따른다고 가정하지만 실제 데이터들은 왜도가 양수이거나 첨도가 양수인 경우가 많다. 본 논문에서는 품질특성치가 정규분포를 따르지 않은 경우에 가짜 알람률 (false alarm rate; FAR)을 이용하여 단일 관리도 성능을 비교하였다. 고려된 단일 관리도는 반원관리도, 최대 관리도 및 평균제곱오차관리도이며 모의실험 결과, 공정이 안정 상태인 경우는 최대관리도의 성능이 좋았으며, 공정이 불안정상태인 경우에는 왜도가 양수일 때 최대관리도, 첨도가 큰 경우에는 평균제곱오차 관리도의 성능이 우수하였다.

• 응용통계연구
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• 제20권3호
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• pp.561-571
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• 2007

국소선형회귀모형의 추정량은 좋은 특성을 가지고 있는 추정량으로서 가장 흔히 사용되는 비모수적 회귀모형의 추정량이라고 하겠다. 이러한 국소선형 추정량이 자료가 희박한 구간에서는 심하게 왜곡된 추정결과를 보이는 문제가 있으며, Hall과 Turlach(1997)이 제안한 선형보간법이 이러한 문제에 대한 매우 효과적인 해결방안이라는 것은 잘 알려진 사실이다. 그러나 Hall과 Turlach가 제안한 선형보간법이 이상값에 매우 취약하다는 사실은 아직 지적된 적이 없는 문제이다. 이 논문에서는 이상값의 영향력을 감소시킬 수 있는 수정된 선형보간법에 의한 유사자료의 생성방법을 제안하고, 그 특성을 모의실험을 통하여 기존의 방법과 비교하였다.

• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.347-366
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• 2001

Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions. The test statistics are generalizations of the Hellinger deviance test of Simpson(1989) and disparity tests of Lindsay(1994), obtained by looking at a 'penalized' version of the distances; harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells. The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test. Also, the tests based on the penalized distances are improvements over those based on the ordinary distances in that they are much closer to the likelihood ratio tests at the null and their convergence to the x$^2$ distribution appears to be dramatically faster; extensive simulation results show that the improvement in performance of the tests due to the penalty is often substantial in small samples.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.123-132
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• 1998

Robust design is an approach to reducing performance variation of quality characteristic values in quality engineering. Taguchi has an idea that mean and variation are handled simultaneously to reduce the expected loss in products. Taguchi parameter design has a great deal of advantages but it also has some disadvantages. The various research efforts aimed at developing alternative methods.