• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.574-574
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• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.575-583
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• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.193-211
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• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

• 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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• 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.

• 품질경영학회지
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• 제17권2호
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• pp.70-80
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• 1989

A nonparametric test for testing the parallelism of regression lines against ordered alternatives is proposed. The proposed test statistic is based on a linear combination of robust slope estimators. It is a modified version of the Adichie's test statistics based on scores. A snail-sample Monte Carlo study shows that the proposed test is compatible with the Adichie's test.

• Journal of the Korean Statistical Society
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• 제7권1호
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.

• Communications for Statistical Applications and Methods
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• 제22권6호
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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.

• Communications for Statistical Applications and Methods
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• 제26권2호
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• pp.149-161
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• 2019

In this article, we suggest the following approaches to simultaneous variable selection and outlier detection. First, we determine possible candidates for outliers using properties of an intercept estimator in a difference-based regression model, and the information of outliers is reflected in the multiple regression model adding mean shift parameters. Second, we select the best model from the model including the outlier candidates as predictors using stochastic search variable selection. Finally, we evaluate our method using simulations and real data analysis to yield promising results. In addition, we need to develop our method to make robust estimates. We will also to the nonparametric regression model for simultaneous outlier detection and variable selection.

• Journal of the Korean Data and Information Science Society
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• 제24권1호
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• pp.33-39
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• 2013

반응변수의 변환을 고려하는 부분선형모형에서 이상치 문제는 선형모형에서와 마찬가지로 반응변수 변환모수의 추정에 왜곡된 결과를 초래할 수 있다. 이를 해결하기 위해서는 부분선형모형에서 반응변수 변환 모수 추정과 이상치 탐지 과정이 수행되어야 하지만 모형에 포함된 비모수 함수의 비정형성에 따른 어려움이 크다. 본 연구에서는 부분선형모형의 비모수함수에 대한 추정과 순차적 검정, 최대절사우도추정 등과 같은 이상치 제거방법의 적용을 통하여 부분선형모형에서 이상치에 강건한 반응변수 변환 과정을 제안한다. 제안된 방법들은 모의실험과 예제를 통해 효과를 비교 검증한다.