文章基本信息

标题：Distribution-free properties of isotonic regression
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作者：Jake A. Soloff ; Adityanand Guntuboyina ; Jim Pitman 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：3243-3253
DOI：10.1214/19-EJS1594
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Shape-constrained regression; statistical dimension; convex minorant; fluctuation theory; quantiles of stochastic processes