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A general asymptotic scheme for inference under order restrictions

Anevski, Dragi LU and Hössjer, Ola LU (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:
author
organization
publishing date
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
Inst 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
2007-12-20 14:23:03
date last changed
2019-04-30 02:33:51
@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},
  keyword      = {monotone,convex,estimation,dependence,regression function,density estimation,limit distributions},
  language     = {eng},
  number       = {4},
  pages        = {1874--1930},
  publisher    = {Inst Mathematical Statistics},
  series       = {Annals of Statistics},
  title        = {A general asymptotic scheme for inference under order restrictions},
  url          = {http://dx.doi.org/10.1214/009053606000000443},
  volume       = {34},
  year         = {2006},
}