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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**DOI**: 10.5282/edoc.6436

### Abstract

Many areas of applied statistics have become aware of the problem of measurement error-prone variables and their appropriate analysis. Simply ignoring the error in the analysis usually leads to biased estimates, like e.g. in the regression with error-prone 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 so-called relevance vector machine (RVM) for nonparametric regression - now enhanced by correction methods based on the ideas of regression calibration, the so-called 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 error-prone 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: | Theses (Dissertation, LMU Munich) |
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Keywords: | Nonparametric regression, Covariate Measurement error, Bayesian methods |

Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 18. July 2006 |

1. Referee: | Augustin, Thomas |

MD5 Checksum of the PDF-file: | 44aefa447eb4672bfa2d3fc1dd628ebb |

Signature of the printed copy: | 0001/UMC 15902 |

ID Code: | 6436 |

Deposited On: | 26. Jan 2007 |

Last Modified: | 24. Oct 2020 08:47 |