Advances in seeded dimension reduction: Bootstrap criteria and extensions

A seeded dimension reduction approach recently developed provides a paradigm to enable existing dimension reduction methods for the central subspace to be adapted to regressions with n<p. The approach is based on successive projection of a seed matrix on a subspace to contain the central subspace. In the article, we will suggest a bootstrap determination procedure to select a proper value for terminating the projections. Also, extensions of seeded dimension reduction are proposed to cover more various types of regressions with n<p such as a categorical predictor regression and survival regression. Then we apply the new development to analyze diffuse large-B-cell lymphoma data and leukemia data. Numerical studies are also presented.