On histogram-based regression and classification with incomplete data

Eric Han () and Majid Mojirsheibani ()
Additional contact information
Eric Han: California State University Northridge
Majid Mojirsheibani: California State University Northridge

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 5, No 2, 635-662

Abstract: Abstract We consider the problem of nonparametric regression with possibly incomplete covariate vectors. The proposed estimators, which are based on histogram methods, are fully nonparametric and straightforward to implement. The presence of incomplete covariates is handled by an inverse weighting method, where the weights are estimates of the conditional probabilities of having incomplete covariate vectors. We also derive various exponential bounds on the $$L_1$$ L 1 norms of our estimators, which can be used to establish strong consistency results for the corresponding, closely related, problem of nonparametric classification with missing covariates. As the main focus and application of our results, we consider the problem of pattern recognition and statistical classification in the presence of incomplete covariates and propose histogram classifiers that are asymptotically optimal.

Keywords: Local averaging; Incomplete data; Strong consistency; Classification (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-020-00794-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metrik:v:84:y:2021:i:5:d:10.1007_s00184-020-00794-y

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-020-00794-y

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().