Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals

Alexander I. Jordan (), Anja Mühlemann () and Johanna F. Ziegel ()
Additional contact information
Alexander I. Jordan: Heidelberg Institute for Theoretical Studies
Anja Mühlemann: University of Bern
Johanna F. Ziegel: University of Bern

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 3, No 5, 489-514

Abstract: Abstract In general, the solution to a regression problem is the minimizer of a given loss criterion and depends on the specified loss function. The nonparametric isotonic regression problem is special, in that optimal solutions can be found by solely specifying a functional. These solutions will then be minimizers under all loss functions simultaneously as long as the loss functions have the requested functional as the Bayes act. For the functional, the only requirement is that it can be defined via an identification function, with examples including the expectation, quantile, and expectile functionals. Generalizing classical results, we characterize the optimal solutions to the isotonic regression problem for identifiable functionals by rigorously treating these functionals as set-valued. The results hold in the case of totally or partially ordered explanatory variables. For total orders, we show that any solution resulting from the pool-adjacent-violators algorithm is optimal.

Keywords: Order-restricted optimization problems; Partial order; Simultaneous optimality; Pool-adjacent-violators algorithm; Consistent loss functions (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-021-00808-0 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:aistmt:v:74:y:2022:i:3:d:10.1007_s10463-021-00808-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-021-00808-0

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().