Semiparametrically Efficient Method for Enveloped Central Space

Linquan Ma, Jixin Wang, Han Chen and Lan Liu

Journal of the American Statistical Association, 2024, vol. 119, issue 547, 2166-2177

Abstract: The estimation of the central space is at the core of the sufficient dimension reduction (SDR) literature. However, it is well known that the finite-sample estimation suffers from collinearity among predictors. Cook, Helland, and Su proposed the predictor envelope method under linear models that can alleviate the problem by targeting a bigger space—which not only envelopes the central information, but also partitions the predictors by finding an uncorrelated set of material and immaterial predictors. One limitation of the predictor envelope is that it has strong distributional and modeling assumptions and therefore, it cannot be readily used in semiparametric settings where SDR usually nests. In this article, we generalize the envelope model by defining the enveloped central space and propose a semiparametric method to estimate it. We derive the entire class of regular and asymptotically linear (RAL) estimators as well as the locally and globally semiparametrically efficient estimators for the enveloped central space. Based on the connection between predictor envelope and partial least square (PLS), our methods can also be used to calculate the PLS space beyond linearity. In the simulations, our methods are shown to be both robust and accurate for estimating the enveloped central space under different settings. Moreover, the downstream analysis using state-of-the-art methods such as machine learning (ML) methods has the potential to achieve much better predictions. We further illustrate our methods in a heart failure study. Supplementary materials for this article are available online.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2023.2252134 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:119:y:2024:i:547:p:2166-2177

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2023.2252134

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().