Rummel, David (2006): Correction for covariate measurement error in nonparametric regression. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

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Abstract
Many areas of applied statistics have become aware of the problem of measurement errorprone variables and their appropriate analysis. Simply ignoring the error in the analysis usually leads to biased estimates, like e.g. in the regression with errorprone covariates. While this problem has been discussed at length for parametric regression, only few methods exist to handle nonparametric regression under error, which are usually either computer intensive or little effective. This thesis develops new methods achieving the correction quality of state of the art methods while demanding only a trickle of their computing time. These new methods use the socalled relevance vector machine (RVM) for nonparametric regression  now enhanced by correction methods based on the ideas of regression calibration, the socalled SIMEX and Markov Chain Monte Carlo (MCMC) correction. All methods are compared in simulation studies regarding Gaussian, binary and Poisson responses. This thesis also discusses the case of multiple errorprone covariates. Furthermore, a MCMC based correction method for nonparametric regression of binary longitudinal data with covariate measurement error is introduced. This data scenario is often encountered, e.g. in epidemiological applications.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Nonparametric regression, Covariate Measurement error, Bayesian methods 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  18. July 2006 
1. Referee:  Augustin, Thomas 
Persistent Identifier (URN):  urn:nbn:de:bvb:1964365 
MD5 Checksum of the PDFfile:  44aefa447eb4672bfa2d3fc1dd628ebb 
Signature of the printed copy:  0001/UMC 15902 
ID Code:  6436 
Deposited On:  26. Jan 2007 
Last Modified:  19. Jul 2016 16:21 