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Nonparametric Functional Estimation under Order Restrictions

Anevski, Dragi LU (2000) In Doctoral Theses in Mathematical Sciences 2000:1.
Abstract
This thesis consists of three papers (Papers A-C) on problems in nonparametric functional estimation, in particular density and regression function estimation and deconvolution, under order assumptions. Pointwise limit distribution results are stated for the obtained estimators, which include isotonic regression estimates, nonparametric maximum likelihood estimates of monotone densities, estimates of convex regression and density functions and deconvolution estimates.



Paper A states a limit distribution formula for the greatest convex minorant mapping and its derivative, which is then applied to regression function and density function estimation under monotonicity or convexity restrictions, at points of continuity and... (More)
This thesis consists of three papers (Papers A-C) on problems in nonparametric functional estimation, in particular density and regression function estimation and deconvolution, under order assumptions. Pointwise limit distribution results are stated for the obtained estimators, which include isotonic regression estimates, nonparametric maximum likelihood estimates of monotone densities, estimates of convex regression and density functions and deconvolution estimates.



Paper A states a limit distribution formula for the greatest convex minorant mapping and its derivative, which is then applied to regression function and density function estimation under monotonicity or convexity restrictions, at points of continuity and under various smoothness assumptions on the unknown function. Also treated is isotonization of kernel estimates, with application to regression and density estimation. Paper B extends the results of Paper A to limit results at points of discontinuity of the unknown function. Paper C is concerned with deconvolution under order restrictions.



Our methods give a unified approach to regression and density function estimation with order restrictions, thereby restating many previously known results as special cases as well as obtaining new results, mainly for dependent data and/or discontinuous functions. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Gill, Richard, Universiteit Utrecht, Dept. of Mathematics, Richard.Gill@math.uu.nl
organization
publishing date
type
Thesis
publication status
published
subject
keywords
monotonicity, convexity, deconvolution, kernel smoothing, NPMLE, long range dependence, greatest convex minorant, mixing, Density estimation, limit distribution., regression, Mathematics, Matematik
in
Doctoral Theses in Mathematical Sciences
volume
2000:1
pages
137 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Centre for Mathematical Sciences, Sölvegatan 18, room MH:A
defense date
2000-04-07 10:15
external identifiers
  • other:ISRN LUNFD6/NFMS--00/1010--SE
ISSN
1404-0034
ISBN
91-628-4062-2
language
English
LU publication?
yes
id
16ea07b5-a255-400d-b13f-1a61e195bd76 (old id 40354)
date added to LUP
2007-06-20 10:53:03
date last changed
2016-09-19 08:44:53
@phdthesis{16ea07b5-a255-400d-b13f-1a61e195bd76,
  abstract     = {This thesis consists of three papers (Papers A-C) on problems in nonparametric functional estimation, in particular density and regression function estimation and deconvolution, under order assumptions. Pointwise limit distribution results are stated for the obtained estimators, which include isotonic regression estimates, nonparametric maximum likelihood estimates of monotone densities, estimates of convex regression and density functions and deconvolution estimates.<br/><br>
<br/><br>
Paper A states a limit distribution formula for the greatest convex minorant mapping and its derivative, which is then applied to regression function and density function estimation under monotonicity or convexity restrictions, at points of continuity and under various smoothness assumptions on the unknown function. Also treated is isotonization of kernel estimates, with application to regression and density estimation. Paper B extends the results of Paper A to limit results at points of discontinuity of the unknown function. Paper C is concerned with deconvolution under order restrictions.<br/><br>
<br/><br>
Our methods give a unified approach to regression and density function estimation with order restrictions, thereby restating many previously known results as special cases as well as obtaining new results, mainly for dependent data and/or discontinuous functions.},
  author       = {Anevski, Dragi},
  isbn         = {91-628-4062-2},
  issn         = {1404-0034},
  keyword      = {monotonicity,convexity,deconvolution,kernel smoothing,NPMLE,long range dependence,greatest convex minorant,mixing,Density estimation,limit distribution.,regression,Mathematics,Matematik},
  language     = {eng},
  pages        = {137},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Nonparametric Functional Estimation under Order Restrictions},
  volume       = {2000:1},
  year         = {2000},
}