• 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.

• 응용통계연구
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• 제23권6호
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• pp.1245-1253
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• 2010

There are two main approaches for estimating the discontinuous regression function nonparametrically. One is the direct approach, the other is the indirect approach. The major goal of the two approaches are different. The direct approach focuses on the overall good estimation of the regression function itself, whereas the indirect approach focuses on the good estimation of jump locations. Apparently, the two approaches are quite different in nature. Gijbels et al. (2007) argue that the comparison of two approaches does not make much sense and that it is even difficult to choose an appropriate criterion for comparisons. However, it is obvious that the indirect approach also has the regression curve estimate as the subsidiary result. Therefore it is necessary to verify the appropriateness of the indirect approach as the estimator of the discontinuous regression function itself. Park (2009a) compared the performance of two approaches through a simulation study. In this paper, we consider a more general case and draw some useful conclusions.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.519-528
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• 2009

This paper deals with nonparametric estimation of discontinuous regression curve. Quite number of researches about this topic have been done. These researches are classified into two categories, the indirect approach and direct approach. The major goal of the indirect approach is to obtain good estimates of jump locations, whereas the major goal of the direct approach is to obtain overall good estimate of the regression curve. Thus it seems that two approaches are quite different in nature, so people say that the comparison of two approaches does not make much sense. Therefore, a thorough comparison of them is lacking. However, even though the main issue of the indirect approach is the estimation of jump locations, it is too obvious that we have an estimate of regression curve as the subsidiary result. The point is whether the subsidiary result of the indirect approach is as good as the main result of the direct approach. The performance of two approaches is compared through a simulation study and it turns out that the indirect approach is a very competitive tool for estimating discontinuous regression curve itself.