It is not unusual for the response variable in a regression model to be subject to censoring or truncation. Tobit regression models are specific examples of such a situation, where for some observations the observed response is not the actual response, but the censoring value (often zero), and an indicator that censoring (from below) has occurred. It is well-known that the maximum likelihood es...

The advance of high-throughput next-generation sequencing technology makes possible the analysis of rare variants. However, the investigation of rare variants in unrelated-individuals data sets faces the challenge of low power, and most methods circumvent the difficulty by using various collapsing procedures based on genes, pathways, or gene clusters. We suggest a new way to identify causal rar...

An Investigation of Sliced Inverse Regression with Censored Data Daniel Riggs August,62010 The complexity of high-dimensional data creates a number of concerns when trying to analyze it. This data often consists of a response or survival time and potentially thousands of predictors. These predictors can be highly correlated, and the sample size is often very small and right censored. Sliced inv...

A generalization of Sliced Inverse Regression to functional regressors was introduced by Ferré and Yao (2003). Here we first address the issue of the identifiability of the Effective Dimension Reduction (EDR) space. Next, we estimate the covariance operator of the conditional expectation by means of kernel estimates. Consistency is proved and this extends the results of Zhu and Fang (1996) in t...

Sliced inverse regression (Duan and Li (1991), Li (1991)) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferré and Yao (2003, 2005) and Hsing and Ren (2009) to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regr...

Graphical methods based on dimension-reduction subspaces for regression problems (Cook 1994) may be useful for studying the relative importance of inputs in computer models of physical systems. Sliced inverse regression (Li 1991), principal Hessian directions (Li 1992), ceres plots (Cook 1993), and inverse response plots (Cook and Weisberg 1994) are recent methods that can identify characterist...

Although the concept of sufficient dimension reduction has been proposed for a long time, studies in the literature have largely focused on properties of estimators of dimension-reduction subspaces in the classical “small p, and large n” setting. Rather than the subspace, this paper considers directly the set of reduced predictors, which we believe are more relevant for subsequent analyses, and...