ContinuousTime Models in Kernel Smoothing
(1999) In Doctoral Theses in Mathematical Sciences 1999:5. Abstract
 This thesis consists of five papers (Papers AE) treating problems in nonparametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers AD) and regression analysis (Paper E). A recurrent theme is to, instead of treating highly positively correlated data as ``asymptotically independent'', take advantage of local dependence structures by using continuoustime models.
In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuoustime multivariate stationary process and relate convergence rates to the local character of the sample paths. This is in Paper B applied to automatic selection of smoothing parameter... (More)  This thesis consists of five papers (Papers AE) treating problems in nonparametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers AD) and regression analysis (Paper E). A recurrent theme is to, instead of treating highly positively correlated data as ``asymptotically independent'', take advantage of local dependence structures by using continuoustime models.
In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuoustime multivariate stationary process and relate convergence rates to the local character of the sample paths. This is in Paper B applied to automatic selection of smoothing parameter of the estimators. In Paper C we study a continuoustime version of a leastsquares crossvalidation approach to selecting smoothing parameter, and the impact the dependence structure of data has on the algorithm. A correction factor is introduced to improve the methods performance for dependent data. Papers D and E treats two statistical inverse problems where the interesting data are not directly observable. In Paper D we consider the problem of estimating the density of a stochastic process from noisy observations. We introduce a method of smoothing the errors and show that by a suitably chosen sampling scheme the convergence rate of independent data methods can be improved upon. Finally in Paper E we treat a problem of nonparametric regression analysis when data is sampled with a sizebias. Our method covers a wider range of practical situations than previously studied methods and by viewing the problem as a locally weighted leastsquares regression problem, extensions to higher order polynomial estimators are straightforward. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/19290
 author
 Sköld, Martin ^{LU}
 supervisor
 opponent

 Prof. Bosq, Denis, Paris VI, France.
 organization
 publishing date
 1999
 type
 Thesis
 publication status
 published
 subject
 keywords
 deconvolution, errorsinvariables, continuous time, dependent data, bandwidth selection, asymptotic variance, Density estimation, kernel smoothing, size bias., Mathematics, Matematik
 in
 Doctoral Theses in Mathematical Sciences
 volume
 1999:5
 pages
 100 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 defense location
 Centre for Mathematical Sciences MH:B
 defense date
 19991112 10:15:00
 external identifiers

 other:LUNFMS10091999
 ISSN
 14040034
 ISBN
 9162838121
 language
 English
 LU publication?
 yes
 id
 7f330c7a99804d099e9232f4b625b6b1 (old id 19290)
 date added to LUP
 20160401 15:31:42
 date last changed
 20190521 13:26:20
@phdthesis{7f330c7a99804d099e9232f4b625b6b1, abstract = {{This thesis consists of five papers (Papers AE) treating problems in nonparametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers AD) and regression analysis (Paper E). A recurrent theme is to, instead of treating highly positively correlated data as ``asymptotically independent'', take advantage of local dependence structures by using continuoustime models.<br/><br> <br/><br> In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuoustime multivariate stationary process and relate convergence rates to the local character of the sample paths. This is in Paper B applied to automatic selection of smoothing parameter of the estimators. In Paper C we study a continuoustime version of a leastsquares crossvalidation approach to selecting smoothing parameter, and the impact the dependence structure of data has on the algorithm. A correction factor is introduced to improve the methods performance for dependent data. Papers D and E treats two statistical inverse problems where the interesting data are not directly observable. In Paper D we consider the problem of estimating the density of a stochastic process from noisy observations. We introduce a method of smoothing the errors and show that by a suitably chosen sampling scheme the convergence rate of independent data methods can be improved upon. Finally in Paper E we treat a problem of nonparametric regression analysis when data is sampled with a sizebias. Our method covers a wider range of practical situations than previously studied methods and by viewing the problem as a locally weighted leastsquares regression problem, extensions to higher order polynomial estimators are straightforward.}}, author = {{Sköld, Martin}}, isbn = {{9162838121}}, issn = {{14040034}}, keywords = {{deconvolution; errorsinvariables; continuous time; dependent data; bandwidth selection; asymptotic variance; Density estimation; kernel smoothing; size bias.; Mathematics; Matematik}}, language = {{eng}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, school = {{Lund University}}, series = {{Doctoral Theses in Mathematical Sciences}}, title = {{ContinuousTime Models in Kernel Smoothing}}, volume = {{1999:5}}, year = {{1999}}, }