• Communications of the Korean Mathematical Society
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• v.19 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.803-810
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• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.327-333
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• 2022

Principal component analysis (PCA) is the most widely used technique in dimension reduction, however, it is very sensitive to outliers. A robust version of PCA, called robust PCA, was suggested by two seminal papers by Candès et al. (2011) and Chandrasekaran et al. (2011). The robust PCA is an essential tool in the artificial intelligence such as background detection, face recognition, ranking, and collaborative filtering. Also, the robust PCA receives a lot of attention in statistics in addition to computer science. In this paper, we introduce recent algorithms for the robust PCA and give some illustrative examples.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.257-262
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• 2003

We introduce a new robust regression estimator, self-tuning regression estimator. Various robust estimators have been developed with discovery for theories and applications since Huber introduced M-estimator at 1960's. We start by announcing various robust estimators and their properties, including their advantages and disadvantages, and furthermore, new estimator overcomes drawbacks of other robust regression estimators, such as ineffective computation on preserving robustness properties.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.659-667
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• 2013

If the regression model or the propensity model is correct, the unbiasedness of the estimator using doubly robust imputation can be guaranteed. Using a neural network instead of a logistic regression model for the propensity model, the estimators using doubly robust imputation are approximately unbiased even though both assumed models fail. We also propose a doubly robust estimator of ratio form using population information of an auxiliary variable. We prove some properties of proposed theory by restricted simulations.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.325-335
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• 2002

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the center of symmetric and continuous underlying distributions. This selector statistics is based on the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying distributions. In this paper, we use the functions of sample quantiles as selector statistics and determine the suitable quantile points based on maximizing the distance index to discriminate distributions under consideration. In Monte Carlo study, this robust estimation method works pretty good in wide range of underlying distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2004.04a
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• pp.131-139
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• 2004

Robust parameter design is to identify appropriate settings of control factors that make the system's performance robust to changes in the noise factors that represent the source of variation. In this paper, we introduce a factor analysis approach to simultaneously optimize multiple quality characteristics in the robust parameter design. An example is illustrated to compare it with already proposed method.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.147-155
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• 1991

This paper treats a robust design criterion which minimizes the effects of outliers and model inadequacy, and investigates robust designs for some response surface designs. In order to develop a robust design criterion and robust design, the integrated mean squared error of *(equation omitted) over a region is utilized, where *(equation omitted). is the estimated response by the minimum bias estimation proposed by carson, Manson and Hader (1969) . According to the number of aberrant observations and their positions, the proposed criterion and designs are studied. Also further development of the proposed criterion is treated when outliers can occur in any position of a design.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1309-1317
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• 2006

The paper considers some Bayes estimators of the finite population mean with auxiliary information under priors which are scale mixtures of normal, and thus have tail heavier than that of the normal. The proposed estimators are quite robust in general. Numerical methods of finding Bayes estimators under these heavy tailed priors are given, and are illustrated with an actual example.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.543-556
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• 2015

We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.