Distributionfree properties of isotonic regression
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 nonasymptotic formula for the squared error risk of least squares in isotonic regression when the true sequence is constant that holds for every exchangeable error distribution.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.04249
 Bibcode:
 2018arXiv181204249S
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability