Continuous-Time Models in Kernel Smoothing
(1999) In Doctoral Theses in Mathematical Sciences 1999:5.- Abstract
- This thesis consists of five papers (Papers A-E) treating problems in non-parametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers A-D) 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 continuous-time models.
In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuous-time 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 A-E) treating problems in non-parametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers A-D) 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 continuous-time models.
In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuous-time 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 continuous-time version of a least-squares cross-validation 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 non-parametric regression analysis when data is sampled with a size-bias. Our method covers a wider range of practical situations than previously studied methods and by viewing the problem as a locally weighted least-squares 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, errors-in-variables, 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
- 1999-11-12 10:15:00
- external identifiers
-
- other:LUNFMS-1009-1999
- ISSN
- 1404-0034
- ISBN
- 91-628-3812-1
- language
- English
- LU publication?
- yes
- id
- 7f330c7a-9980-4d09-9e92-32f4b625b6b1 (old id 19290)
- date added to LUP
- 2016-04-01 15:31:42
- date last changed
- 2019-05-21 13:26:20
@phdthesis{7f330c7a-9980-4d09-9e92-32f4b625b6b1,
abstract = {{This thesis consists of five papers (Papers A-E) treating problems in non-parametric statistics, especially methods of kernel smoothing applied to density estimation for stochastic processes (Papers A-D) 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 continuous-time models.<br/><br>
<br/><br>
In Papers A and B we derive expressions for the asymptotic variance of the kernel density estimator of a continuous-time 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 continuous-time version of a least-squares cross-validation 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 non-parametric regression analysis when data is sampled with a size-bias. Our method covers a wider range of practical situations than previously studied methods and by viewing the problem as a locally weighted least-squares regression problem, extensions to higher order polynomial estimators are straightforward.}},
author = {{Sköld, Martin}},
isbn = {{91-628-3812-1}},
issn = {{1404-0034}},
keywords = {{deconvolution; errors-in-variables; 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 = {{Continuous-Time Models in Kernel Smoothing}},
volume = {{1999:5}},
year = {{1999}},
}