Distribution-free properties of isotonic regression
Authors:
- Jake A. SoloffJSJake A. Soloff
- Adityanand GuntuboyinaAGAdityanand Guntuboyina
- Jim PitmanJPJim Pitman
Open Access
- 1 January 2019
- journal article
- research article
- Published by Institute of Mathematical Statistics in Electronic Journal of Statistics
- Vol. 13 (2) , 3243-3253
Abstract
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.Keywords
All Related Versions
This publication has 14 references indexed in Scilit:
- On the risk of convex-constrained least squares estimators under misspecificationBernoulli, 2019
- Nonparametric Shape-Restricted RegressionStatistical Science, 2018
- Sharp oracle inequalities for Least Squares estimators in shape restricted regressionThe Annals of Statistics, 2018
- Sharp MSE Bounds for Proximal DenoisingFoundations of Computational Mathematics, 2015
- Living on the edge: phase transitions in convex programs with random dataInformation and Inference: A Journal of the IMA, 2014
- Estimation of a Convex Function: Characterizations and Asymptotic TheoryThe Annals of Statistics, 2001
- Marginal Densities of the Least Concave Majorant of Brownian MotionThe Annals of Statistics, 2001
- Projections onto order simplexesApplied Mathematics & Optimization, 1984
- Projections on Convex Sets in Hilbert Space and Spectral Theory: Part I. Projections on Convex Sets: Part II. Spectral Theory1971
- The circumference of a convex polygonProceedings of the American Mathematical Society, 1961