We revisit cumulative slicing estimation (CUME; Zhu et al., 2010) from a different perspective to gain more insights, then refine its performance by incorporating the intra-slice covariances. We also prove that our new method, under some conditions, is more comprehensive than CUME.

Classical sufficient dimension reduction methods are sensitive to outliers present in predictors, and may not perform well when the distribution of the predictors is heavy-tailed. In this paper, we propose two robust inverse regression methods which are insensitive to data contamination:...

A number of studies have explored the semi- and nonparametric estimation of stochastic frontier models by using kernel regression or other nonparametric smoothing techniques. In contrast to popular deterministic nonparametric estimators, these approaches do not allow one to impose any shape...

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...