Consistency of Concave Regression with an Application to Current-Status Data

Dümbgen, Lutz; Freitag, Sandra; Jongbloed, Geurt (2004). Consistency of Concave Regression with an Application to Current-Status Data. Mathematical methods of statistics, 13, pp. 69-81. Allerton Press

[img]
Preview
Text
ConcaveRegr.pdf - Accepted Version
Available under License Publisher holds Copyright.

Download (135kB) | Preview

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz

Subjects:

500 Science > 510 Mathematics

ISSN:

1066-5307

Publisher:

Allerton Press

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

14 Dec 2015 09:33

Last Modified:

14 Dec 2015 09:33

BORIS DOI:

10.7892/boris.73748

URI:

https://boris.unibe.ch/id/eprint/73748

Actions (login required)

Edit item Edit item
Provide Feedback