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In "Li, L. and Yin, X. (2008). Sliced Inverse Regression withRegularizations. Biometrics, 64(1):124--131" a ridge SIR estimator isintroduced as the solution of a minimization problem and computed thanks to analternating least-squares algorithm. This methodology reveals good performancein practice. In this note, we focus on the theoretical properties of theestimator. Is it shown that the minimization problem is degenerated in thesense that only two situations can occur: Either the ridge SIR estimator doesnot exist or it is zero.

A Note on Sliced Inverse Regression with Regularizations