Nonparametric efficient estimation of prediction error for incomplete data models

Commonly accepted measures of prediction error, such as mean squared <br>error or R^2 typically fail to be identifiable with censored <br>observations. The Brier score is a loss function which is suitable for <br>the assessment of predictions made in terms of predicted probabilities <br>that are coming from a regression model or other sources. <br> <br>This thesis is on defining and estimating measures of prediction error <br>based on the Brier score. Function valued parameters are introduced <br>which are useful for graphical assessment and comparison of <br>classification schemes. <br> <br>For estimation of prediction error in the presence of censoring, <br>generalized non-parametric information bounds are developed. For <br>predictions of survival probabilities that may depend on a vector of <br>covariates, it is proved that inverse probability of censoring <br>weighted estimators are consistent and asymptotically efficient. Here, <br>different assumptions on the censoring mechanism are carefully <br>studied. The methods used involve a version of the well-known delta <br>method which is suitably adapted to handle smoothed empirical <br>processes.

Author dc:creator

• Gerds, Thomas

Contributors dc:contributor

• Schumacher, Martin

• Brier score
• Überlebenszeitanalyse
• efficient estimation
• censored data
• prediction error
• survival analysis

Repository record source_url

https://freidok.uni-freiburg.de/data/702

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:702