A theoretical note on optimal sufficient dimension reduction with singularity

Jae Keun Yoo

Statistics & Probability Letters, 2015, vol. 99, issue C, 109-113

Abstract: In this paper, we discuss an optimal sufficient dimension reduction through minimizing a quadratic objective function proposed by Cook and Ni (2005) with singular inner-product matrix. Within a less restrictive class of inner-product matrices, a generalized inverse of the consistent estimator of the asymptotic covariance matrix gives us the benefit of χ2 statistic and asymptotic efficiency within a subclass.

Keywords: χ2 test; Minimum discrepancy approach; Singularity; Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.01.004

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