Trial Lecture – time and place
See Trial Lecture.
Adjudication committee
- First opponent: Professor Malka Gorfine, Tel Aviv University
- Second opponent: Associate Professor Alessandra Rosalba Brazzale, University of Padova
- Third member and chair of the evaluation committee: Associate Professor Torbjørn Wisløff, University of Oslo
Chair of the Defence
Head of Institute Lene Frost Andersen, University of Oslo
Principal Supervisor
Professor Magne Thoresen, University of Oslo
Summary
In almost all disciplines, it may not be possible to observe a variable accurately, for some reason, and therefore it is necessary to work with an error-prone version of that variable. When measurement error is present among the covariates of a regression model it can cause bias in the parameter estimation, interfere with variable selection and lead to a loss of power and to trouble in detecting the true relationship among variables.
A plethora of correction methods for measurement error in both linear and non-linear models is available. However, inference can still be challenging for a variety of reasons. Additionally, most of the corrected estimators, despite being consistent or approximately consistent under certain conditions, are slightly biased.
In this thesis, we explore the use of the model-based bootstrap, a powerful method that allows for inference when analytical alternatives are not available, when correcting for measurement error. We suggest new methodologies that not only offer some definitive advantages over the simple bootstrap and other standard methods, but also are able to estimate the bias of the corrected estimators.
In regression theory, construction of confidence intervals and hypothesis testing rely on homoscedasticity of the model error. In this thesis, we explore heteroscedasticity detection and correction under the presence of measurement error. We compare the available methods for residual analysis, we present a developed model-based bootstrap test for heteroscedasticity, and we show how modelling heteroscedasticity can affect prediction intervals.
As a final goal of the thesis, we explore penalized regression methods that can correct for measurement error in a high-dimensional context. We evaluate these methods and focus on situations that are relevant in a practical application context, where the measurement error distribution and dependence structure are not known and need to be estimated from the data.
Additional information
Contact the research support staff.