A review on the generalization of sufficient dimension reduction methods with the additional information. (24th May 2017) - Hung, Hung; Lu, Henry Horng‐Shing
Abstract : Sufficient dimension reduction (SDR) has been shown to be a powerful statistical method that is able to reduce the dimension of covariates without losing information with respect to the response. Subsequent analysis can then be based on a lower dimensional transformations of covariates, which has the potential to assist model building and to increase the estimation efficiency. In some situations, the additional information could be also available during the data collection process. Although one can proceed with the conventional method, properly utilizing the additional information can greatly improve making statistical inference. It is thus of interest to incorporate the additional information into the practice of SDR methods. In this article, we review the generalizations of SDR methods that are able to utilize different types of the additional information. One will see that, depending on the sources of the additional information, different techniques are required to modify conventional SDR methods to improve estimating the target of interest. WIREs Comput Stat 2017, 9:e1401. doi: 10.1002/wics.1401 This article is categorized under: Applications of Computational Statistics > Computational Mathematics Applications of Computational Statistics > Computational and Molecular Biology Statistical and Graphical Methods of Data Analysis > Dimension Reduction Abstract : Sufficient dimension reduction (SDR) is a powerful statistical method that is able to reduce the dimension of covariates (from X to Γ T X ) without losing information with respect to the response Y . In some situations, different sources of additional information are also available during the data collection process. It is of interest to incorporate the additional information in to the practice of SDR methods, to enhance the estimation of S Y | X .