Regression Analysis of Censored Data with Applications in Perimetry
(1999) In Doctoral Theses in Mathematical Sciences Abstract
 This thesis treats regression analysis when either the dependent or the independent variable is censored. We deal with quantile regression when the dependent variable is censored. Using the independence between the true values and the censoring limits the quantile function for the true values can be rewritten as another quantile function of the observed, censored values, where the quantile value itself is a function of the censoring distribution. The quantile value is estimated nonparametrically and the properties of the resulting quantile function estimate studied by simulations. We also apply this technique in practice to the problem of finding limits for the normal variability in stable glaucomatous visual fields.
... (More)  This thesis treats regression analysis when either the dependent or the independent variable is censored. We deal with quantile regression when the dependent variable is censored. Using the independence between the true values and the censoring limits the quantile function for the true values can be rewritten as another quantile function of the observed, censored values, where the quantile value itself is a function of the censoring distribution. The quantile value is estimated nonparametrically and the properties of the resulting quantile function estimate studied by simulations. We also apply this technique in practice to the problem of finding limits for the normal variability in stable glaucomatous visual fields.
When the independent variable is censored it is possible to achieve estimates by throwing away the censored data and estimate the mean function by ordinary least squares using only the noncensored data. We try to improve on these estimates by redistribution the censored values to positions based on the value of the dependent variable and the estimated distribution of the independent variable conditional on the fact that it is censored. The distributions are estimated in three different ways, parametrically, assuming, e.g. a twodimensional normal distribution, semiparametrically, assuming a normal distribution for the dependent variable given the independent one while estimating the distribution of the independent variable nonparametrically, and nonparametrically estimating the distribution of the independent variable locally in a band around the value of the dependend variable. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/39438
 author
 Lindgren, Anna ^{LU}
 supervisor
 opponent

 Professor Fellman, Johan, Swedish School of Economics, Helsinki, Finland
 organization
 publishing date
 1999
 type
 Thesis
 publication status
 published
 subject
 keywords
 censored covariate, L_1 minimization, rightcensoring, Quantile regression
 in
 Doctoral Theses in Mathematical Sciences
 pages
 120 pages
 publisher
 Mathematical Statistics, Centre for Mathematical Sciences, Lund University
 defense location
 Centre for Mathematical Sciences, MH:A
 defense date
 19990423 10:15:00
 external identifiers

 other:ISRN: LUNFMS10081999
 ISSN
 14040034
 ISBN
 9162834991
 language
 English
 LU publication?
 yes
 id
 319ec3d19a35432382b9dff47cabec71 (old id 39438)
 date added to LUP
 20160401 16:39:19
 date last changed
 20190521 13:40:25
@phdthesis{319ec3d19a35432382b9dff47cabec71, abstract = {{This thesis treats regression analysis when either the dependent or the independent variable is censored. We deal with quantile regression when the dependent variable is censored. Using the independence between the true values and the censoring limits the quantile function for the true values can be rewritten as another quantile function of the observed, censored values, where the quantile value itself is a function of the censoring distribution. The quantile value is estimated nonparametrically and the properties of the resulting quantile function estimate studied by simulations. We also apply this technique in practice to the problem of finding limits for the normal variability in stable glaucomatous visual fields.<br/><br> <br/><br> When the independent variable is censored it is possible to achieve estimates by throwing away the censored data and estimate the mean function by ordinary least squares using only the noncensored data. We try to improve on these estimates by redistribution the censored values to positions based on the value of the dependent variable and the estimated distribution of the independent variable conditional on the fact that it is censored. The distributions are estimated in three different ways, parametrically, assuming, e.g. a twodimensional normal distribution, semiparametrically, assuming a normal distribution for the dependent variable given the independent one while estimating the distribution of the independent variable nonparametrically, and nonparametrically estimating the distribution of the independent variable locally in a band around the value of the dependend variable.}}, author = {{Lindgren, Anna}}, isbn = {{9162834991}}, issn = {{14040034}}, keywords = {{censored covariate; L_1 minimization; rightcensoring; Quantile regression}}, language = {{eng}}, publisher = {{Mathematical Statistics, Centre for Mathematical Sciences, Lund University}}, school = {{Lund University}}, series = {{Doctoral Theses in Mathematical Sciences}}, title = {{Regression Analysis of Censored Data with Applications in Perimetry}}, url = {{https://lup.lub.lu.se/search/files/4736904/1670650.pdf}}, year = {{1999}}, }