Reply to the paper by Liliana Forzani and R. Dennis Cook: "A note on smoothed functional inverse regression"

Ferré and Yao (2005) proposed an approach to the estimation of the Effective Dimension Reduction space in functional sliced inverse regression. This did not require the inversion of the variance-covariance operator of the explanatory variable, and thus circumvent the main drawback of SIR in the functional case. Forzani and Cook (2007) argued that our result is possible only under additional conditions. Although our discussion may have created ambiguity, the result is correct and does not require further assumptions. In this note, we give the additional details needed to make our purpose clear.