• The Korean Journal of Applied Statistics
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• v.35 no.5
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• pp.657-666
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• 2022

An informative predictor subspace is useful to estimate the central subspace, when conditions required in usual suffcient dimension reduction methods fail. Recently, for multivariate regression, Ko and Yoo (2022) newly defined a projective-resampling informative predictor subspace, instead of the informative predictor subspace, by the adopting projective-resampling method (Li et al. 2008). The new space is contained in the informative predictor subspace but contains the central subspace. In this paper, a method directly to estimate the informative predictor subspace is proposed, and it is compapred with the method by Ko and Yoo (2022) through theoretical aspects and numerical studies. The numerical studies confirm that the Ko-Yoo method is better in the estimation of the central subspace than the proposed method and is more efficient in sense that the former has less variation in the estimation.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.431-443
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• 2020

The K-means clustering algorithm has had successful application in sufficient dimension reduction. Unfortunately, the algorithm does have reproducibility and nestness, which will be discussed in this paper. These are clear deficits for the K-means clustering algorithm; however, the hierarchical clustering algorithm has both reproducibility and nestness, but intensive comparison between K-means and hierarchical clustering algorithm has not yet been done in a sufficient dimension reduction context. In this paper, we rigorously study the two clustering algorithms for two popular sufficient dimension reduction methodology of inverse mean and clustering mean methods throughout intensive numerical studies. Simulation studies and two real data examples confirm that the use of hierarchical clustering algorithm has a potential advantage over the K-means algorithm.