A general asymptotic scheme for inference under order restrictions
(2006) In Annals of Statistics 34(4). p.1874-1930- Abstract
- Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/685739
- author
- Anevski, Dragi LU and Hössjer, Ola LU
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- monotone, convex, estimation, dependence, regression function, density estimation, limit distributions
- in
- Annals of Statistics
- volume
- 34
- issue
- 4
- pages
- 1874 - 1930
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- wos:000242314100016
- scopus:33845304314
- ISSN
- 0090-5364
- DOI
- 10.1214/009053606000000443
- language
- English
- LU publication?
- yes
- id
- 18c3e482-dc1f-413e-91ca-f9b83274eff5 (old id 685739)
- date added to LUP
- 2016-04-01 16:18:51
- date last changed
- 2022-02-27 20:19:43
@article{18c3e482-dc1f-413e-91ca-f9b83274eff5, abstract = {{Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.}}, author = {{Anevski, Dragi and Hössjer, Ola}}, issn = {{0090-5364}}, keywords = {{monotone; convex; estimation; dependence; regression function; density estimation; limit distributions}}, language = {{eng}}, number = {{4}}, pages = {{1874--1930}}, publisher = {{Institute of Mathematical Statistics}}, series = {{Annals of Statistics}}, title = {{A general asymptotic scheme for inference under order restrictions}}, url = {{http://dx.doi.org/10.1214/009053606000000443}}, doi = {{10.1214/009053606000000443}}, volume = {{34}}, year = {{2006}}, }