Consistency of Penalized Convex Regression

Eunji Lim

International Journal of Statistics and Probability, 2021, vol. 10, issue 1, 69

Abstract: We consider the problem of estimating an unknown convex function f_* (0, 1)^d →R from data (X1, Y1), … (X_n; Y_n).A simple approach is finding a convex function that is the closest to the data points by minimizing the sum of squared errors over all convex functions. The convex regression estimator, which is computed this way, su ers from a drawback of having extremely large subgradients near the boundary of its domain. To remedy this situation, the penalized convex regression estimator, which minimizes the sum of squared errors plus the sum of squared norms of the subgradient over all convex functions, is recently proposed. In this paper, we prove that the penalized convex regression estimator and its subgradient converge with probability one to f_* and its subgradient, respectively, as n → ∞, and hence, establish the legitimacy of the penalized convex regression estimator.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/ijsp/article/download/0/0/44423/46850 (application/pdf)
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/44423 (text/html)

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:ibn:ijspjl:v:10:y:2021:i:1:p:69

Access Statistics for this article

More articles in International Journal of Statistics and Probability from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().