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The asymptotic distribution of the isotonic regression estimator over a general countable pre-ordered set

Anevski, Dragi LU and Pastukhov, Vladimir LU (2018) In Electronic Journal of Statistics 12(2). p.4180-4208
Abstract

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution of the isotonized estimator is given by the concatenation of the separate isotonic regressions of the certain subvectors of an unrestrecred estimator’s asymptotic distribution. Also, we show that the isotonization preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Constrained inference, Isotonic regression, Limit distribution
in
Electronic Journal of Statistics
volume
12
issue
2
pages
29 pages
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:85063390384
ISSN
1935-7524
DOI
10.1214/18-EJS1507
language
English
LU publication?
yes
id
c3c82754-7512-4446-ad18-f84135b29e90
date added to LUP
2019-04-11 11:26:54
date last changed
2020-01-13 01:39:13
@article{c3c82754-7512-4446-ad18-f84135b29e90,
  abstract     = {<p>We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution of the isotonized estimator is given by the concatenation of the separate isotonic regressions of the certain subvectors of an unrestrecred estimator’s asymptotic distribution. Also, we show that the isotonization preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.</p>},
  author       = {Anevski, Dragi and Pastukhov, Vladimir},
  issn         = {1935-7524},
  language     = {eng},
  number       = {2},
  pages        = {4180--4208},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Electronic Journal of Statistics},
  title        = {The asymptotic distribution of the isotonic regression estimator over a general countable pre-ordered set},
  url          = {http://dx.doi.org/10.1214/18-EJS1507},
  doi          = {10.1214/18-EJS1507},
  volume       = {12},
  year         = {2018},
}