Nonparametric Functional Estimation under Order Restrictions
(2000) In Doctoral Theses in Mathematical Sciences 2000:1. Abstract
 This thesis consists of three papers (Papers AC) 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 AC) 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:
http://lup.lub.lu.se/record/40354
 author
 Anevski, Dragi ^{LU}
 supervisor

 Ola Hössjer ^{LU}
 opponent

 Professor Gill, Richard, Universiteit Utrecht, Dept. of Mathematics, Richard.Gill@math.uu.nl
 organization
 publishing date
 2000
 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
 20000407 10:15
 external identifiers

 other:ISRN LUNFD6/NFMS00/1010SE
 ISSN
 14040034
 ISBN
 9162840622
 language
 English
 LU publication?
 yes
 id
 16ea07b5a255400db13f1a61e195bd76 (old id 40354)
 date added to LUP
 20070620 10:53:03
 date last changed
 20160919 08:44:53
@phdthesis{16ea07b5a255400db13f1a61e195bd76, abstract = {This thesis consists of three papers (Papers AC) 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 = {9162840622}, issn = {14040034}, 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}, }