Correction for covariate measurement error in nonparametric regression

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

Statistical Modelling

The book collects the proceedings of the 19th International Workshop on Statistical Modelling held in Florence on July 2004. Statistical modelling is an important cornerstone in many scientific disciplines, and the workshop has provided a rich environment for cross-fertilization of ideas from different disciplines. It consists in four invited lectures, 48 contributed papers and 47 posters. The contributions are arranged in sessions: Statistical Modelling; Statistical Modelling in Genomics; Semi-parametric Regression Models; Generalized Linear Mixed Models; Correlated Data Modelling; Missing Data, Measurement of Error and Survival Analysis; Spatial Data Modelling and Time Series and Econometrics