Nonparametric Estimation of Conditional Expectation with Auxiliary Information and Dimension Reduction

Bingying Xie and Jun Shao

Journal of the American Statistical Association, 2021, vol. 116, issue 535, 1346-1357

Abstract: Nonparametric estimation of the conditional expectation E(Y|U) of an outcome Y given a covariate vector U is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable Z in the training dataset used to construct estimators, but Z is not available for future prediction or selecting patient treatment in personalized medicine. For example, in the training dataset longitudinal outcomes are observed, but only the last outcome Y is concerned in the future prediction or analysis. The longitudinal outcomes other than the last point is then the variable Z that is observed and related with both Y and U. Previous work on how to make use of Z in the estimation of E(Y|U) mainly focused on using Z in the construction of a linear function of U to reduce covariate dimension for better estimation. Using E(Y|U)=E{E(Y|U,Z)|U} , we propose a two-step estimation of inner and outer expectations, respectively, with sufficient dimension reduction for kernel estimation in both steps. The information from Z is utilized not only in dimension reduction, but also directly in the estimation. Because of the existence of different ways for dimension reduction, we construct two estimators that may improve the estimator without using Z. The improvements are shown in the convergence rate of estimators as the sample size increases to infinity as well as in the finite sample simulation performance. A real data analysis about the selection of mammography intervention is presented for illustration.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2020.1713793 (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:116:y:2021:i:535:p:1346-1357

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

DOI: 10.1080/01621459.2020.1713793

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 ().