Limit properties of the monotone rearrangement for density and regression function estimation
(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:
https://lup.lub.lu.se/record/1494778
- author
- Anevski, Dragi LU and Fougeres, Anne-Laure
- organization
- publishing date
- 2019
- 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
- 2022-03-15 23:10:00
@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}}, keywords = {{Limit distributions; regression function es- timation; monotone rearrangement.; dependence; density estimation}}, 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}}, }