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Limit properties of the monotone rearrangement for density and regression function estimation

Anevski, Dragi LU and Fougeres, Anne-Laure (2019) In Bernoulli 25(1). p.549-583
Abstract
The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Po ́lya as a sorting device for functions. As- suming that x is a monotone function and that an estimate xn of x is given, consider the monotone rearrangement xˆn of xn. This new estimator is shown to be uniformly consistent. Under suitable as- sumptions, pointwise limit distribution results for xˆn are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Limit distributions, regression function es- timation, monotone rearrangement., dependence, density estimation
in
Bernoulli
volume
25
issue
1
pages
43 pages
publisher
Chapman and Hall
external identifiers
  • scopus:85058489601
ISSN
1350-7265
DOI
10.3150/17-BEJ998
language
English
LU publication?
yes
id
664637f1-203e-4d41-811d-1dfe6c7c7047 (old id 1494778)
alternative location
http://arxiv.org/pdf/0710.4617
date added to LUP
2016-04-04 11:23:21
date last changed
2019-02-20 09:18:16
@article{664637f1-203e-4d41-811d-1dfe6c7c7047,
  abstract     = {The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Po ́lya as a sorting device for functions. As- suming that x is a monotone function and that an estimate xn of x is given, consider the monotone rearrangement xˆn of xn. This new estimator is shown to be uniformly consistent. Under suitable as- sumptions, pointwise limit distribution results for xˆn are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.},
  author       = {Anevski, Dragi and Fougeres, Anne-Laure},
  issn         = {1350-7265},
  language     = {eng},
  number       = {1},
  pages        = {549--583},
  publisher    = {Chapman and Hall},
  series       = {Bernoulli},
  title        = {Limit properties of the monotone rearrangement for density and regression function estimation},
  url          = {http://dx.doi.org/10.3150/17-BEJ998},
  doi          = {10.3150/17-BEJ998},
  volume       = {25},
  year         = {2019},
}