Local Polynomial Regression with Application on Lidar Measurements
(2004) Abstract
 This thesis deals with the problem of estimating a function or one of its derivatives from a set of measurements, mainly of a bivariate or spatial nature which is so common in environmental applications. In this work particular attention has been on the lidar (light detection and ranging) application which is a versatile technique for measurement of among other things atmospheric trace gases. In lidar measurements the information about the concentration is carried by the derivative of the meanfunction.
The exclusive tool that is used for estimation of a function or its derivatives in this thesis is local polynomial regression. However, other nonparametric techniques might be possible to use and some of the results... (More)  This thesis deals with the problem of estimating a function or one of its derivatives from a set of measurements, mainly of a bivariate or spatial nature which is so common in environmental applications. In this work particular attention has been on the lidar (light detection and ranging) application which is a versatile technique for measurement of among other things atmospheric trace gases. In lidar measurements the information about the concentration is carried by the derivative of the meanfunction.
The exclusive tool that is used for estimation of a function or its derivatives in this thesis is local polynomial regression. However, other nonparametric techniques might be possible to use and some of the results presented here are indeed of a more general nature. The thesis consists of four papers of which the first and the last are applied to lidar measurements. The other two papers are methodology based with the intention to contribute to and also improve the statistical evaluation of the lidar process.
In the first paper, Paper A, lidar measurements are considered by adopting a univariate model with a nonconstant variancefunction. Evaluation is based on local polynomial regression with automatically selected local bandwidths, both for the derivatives of the meanfunction and for the variancefunction. Paper B presents a method for estimation of spatial covariance fields. Estimation is based on nonparametric techniques and considers covariances as functions of the location with fixed displacements. Paper C considers the problem of selecting local bandwidth matrices for bivariate local polynomial regression. In this paper an automatic bandwidth selector, EBBS<sub>dep</sub>, is developed which allows for correlated errors. Also, a set of MATLAB files for bivariate local polynomial regression based on EBBS<sub>dep</sub>selected bandwidth matrices is developed. Finally, in Paper D the method in Paper C is used to construct estimates of 2D concentration maps of atomic mercury from fields of lidar measurements. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/467353
 author
 Lindström, Torgny ^{LU}
 supervisor
 opponent

 Professor Opsomer, Jean, USA
 organization
 publishing date
 2004
 type
 Thesis
 publication status
 published
 subject
 keywords
 Mathematics, Matematik, differential equations, Funktioner, differentialekvationer, variancefunction estimation., spatial dependence, nonparametric, local polynomial regression, local bandwidth selection, lidar, heteroscedasticity, Bivariate estimation, differential absorption, Functions
 pages
 186 pages
 defense location
 Matematikcentrum, Sölvegatan 18, sal MH:C, Lunds Tekniska Högskola.
 defense date
 20040924 10:15:00
 ISBN
 9162861948
 language
 English
 LU publication?
 yes
 additional info
 Article: T. Lindström, U. Holst, P. Weibring and H. Edner (2002). Analysis of Lidar Measurements using Nonparametric Kernel Regression Methods.Applied Physics B, 74(2):155165. Article: T. Lindström (2003). A Nonparametric Spatial Covariance Estimator.Technical Report, Centre for Mathematical Sciences, Mathematical Statistics, 2003:02. Revised version. Article: T. Lindström (2004). EmpiricalBias Bandwidths for Spatial Local Polynomial Regression with Correlated Errors.Submitted to Journal of Nonparametric Statistics. Article: T. Lindström, U. Holst and P. Weibring (2004). Analysis of Lidar Fields using Local Polynomial Regression.Submitted to Environmetrics.
 id
 50a7328d974a4ce5bce6a3d3c187c648 (old id 467353)
 date added to LUP
 20160404 09:37:02
 date last changed
 20181121 20:54:22
@phdthesis{50a7328d974a4ce5bce6a3d3c187c648, abstract = {This thesis deals with the problem of estimating a function or one of its derivatives from a set of measurements, mainly of a bivariate or spatial nature which is so common in environmental applications. In this work particular attention has been on the lidar (light detection and ranging) application which is a versatile technique for measurement of among other things atmospheric trace gases. In lidar measurements the information about the concentration is carried by the derivative of the meanfunction.<br/><br> <br/><br> The exclusive tool that is used for estimation of a function or its derivatives in this thesis is local polynomial regression. However, other nonparametric techniques might be possible to use and some of the results presented here are indeed of a more general nature. The thesis consists of four papers of which the first and the last are applied to lidar measurements. The other two papers are methodology based with the intention to contribute to and also improve the statistical evaluation of the lidar process.<br/><br> <br/><br> In the first paper, Paper A, lidar measurements are considered by adopting a univariate model with a nonconstant variancefunction. Evaluation is based on local polynomial regression with automatically selected local bandwidths, both for the derivatives of the meanfunction and for the variancefunction. Paper B presents a method for estimation of spatial covariance fields. Estimation is based on nonparametric techniques and considers covariances as functions of the location with fixed displacements. Paper C considers the problem of selecting local bandwidth matrices for bivariate local polynomial regression. In this paper an automatic bandwidth selector, EBBS<sub>dep</sub>, is developed which allows for correlated errors. Also, a set of MATLAB files for bivariate local polynomial regression based on EBBS<sub>dep</sub>selected bandwidth matrices is developed. Finally, in Paper D the method in Paper C is used to construct estimates of 2D concentration maps of atomic mercury from fields of lidar measurements.}, author = {Lindström, Torgny}, isbn = {9162861948}, language = {eng}, school = {Lund University}, title = {Local Polynomial Regression with Application on Lidar Measurements}, year = {2004}, }