Projective resampling estimation of informative predictor subspace for multivariate regression. (English) Zbl 1504.62053
Summary: In this paper, a paradigm to estimate the so-called informative predictor subspace [the second author, Statistics 50, No. 5, 1086–1099 (2016; Zbl 1356.62055)] for multivariate regression is proposed. For this, as a primary target subspace, a projective resampling informative predictor subspace is newly developed. The projective resampling informative predictor subspace is constructed based on a projection resampling method by B. Li et al. [J. Am. Stat. Assoc. 103, No. 483, 1177–1186 (2008; Zbl 1205.62067)], and it has advantage that it is smaller than the original informative predictor subspace but contains the central subspace. To estimate the new target subspace, the three approaches of projective resampling, coordinate, and coordinate-projective resampling mean methods are proposed. The three methods are investigated via various numerical studies, which confirm their potential usefulness in practice.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G09 | Nonparametric statistical resampling methods |
| 62H12 | Estimation in multivariate analysis |
Keywords:
clustering mean method; fused estimation; informative predictor subspace; \(K\)-means clustering; sufficient dimension reductionReferences:
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