Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 2 (2019), 3243-3253.
Distribution-free properties of isotonic regression
It is well known that the isotonic least squares estimator is characterized as the derivative of the greatest convex minorant of a random walk. Provided the walk has exchangeable increments, we prove that the slopes of the greatest convex minorant are distributed as order statistics of the running averages. This result implies an exact non-asymptotic formula for the squared error risk of least squares in homoscedastic isotonic regression when the true sequence is constant that holds for every exchangeable error distribution.
Electron. J. Statist., Volume 13, Number 2 (2019), 3243-3253.
Received: February 2019
First available in Project Euclid: 24 September 2019
Permanent link to this document
Digital Object Identifier
Soloff, Jake A.; Guntuboyina, Adityanand; Pitman, Jim. Distribution-free properties of isotonic regression. Electron. J. Statist. 13 (2019), no. 2, 3243--3253. doi:10.1214/19-EJS1594. https://projecteuclid.org/euclid.ejs/1569290688