On relative universality, regression operator, and conditional independence
相对普适性、回归算子与条件独立
The notion of relative universality with respect to a σ-field was introduced to establish the unbiasedness and Fisher consistency of an estimator in nonlinear sufficient dimension reduction. However, there is a gap in the proof of this result in the existing literature. The existing definition of relative universality seems to be too strong for the proof to be valid. In this note we modify the definition of relative universality using the concept of ǫ-measurability, and…