Directional regression is an effective sufficient dimension reduction method which implicitly synthesizes the first two conditional moments. In this paper, we extend directional regression to a general family of estimators via the notion of general empirical directions. Data-driven method is...

Functional data are infinite-dimensional statistical objects which pose significant challenges to both theorists and practitioners. Both parametric and nonparametric regressions have received attention in the functional data analysis literature. However, the former imposes stringent constraints...

Specifying the structural dimension is an important first step for the sufficient dimension reduction methodology. Based on the popular sequential test approach, we propose a novel test statistic via directional regression to determine the structural dimension in this paper.