{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:702"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:702","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Nonparametric efficient estimation of prediction error for incomplete data models","abstract":"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.","abstract_html":"Commonly accepted measures of prediction error, such as mean squared &lt;br&gt;error or R^2 typically fail to be identifiable with censored &lt;br&gt;observations. The Brier score is a loss function which is suitable for &lt;br&gt;the assessment of predictions made in terms of predicted probabilities &lt;br&gt;that are coming from a regression model or other sources. &lt;br&gt; &lt;br&gt;This thesis is on defining and estimating measures of prediction error &lt;br&gt;based on the Brier score. Function valued parameters are introduced &lt;br&gt;which are useful for graphical assessment and comparison of &lt;br&gt;classification schemes. &lt;br&gt; &lt;br&gt;For estimation of prediction error in the presence of censoring, &lt;br&gt;generalized non-parametric information bounds are developed. For &lt;br&gt;predictions of survival probabilities that may depend on a vector of &lt;br&gt;covariates, it is proved that inverse probability of censoring &lt;br&gt;weighted estimators are consistent and asymptotically efficient. Here, &lt;br&gt;different assumptions on the censoring mechanism are carefully &lt;br&gt;studied. The methods used involve a version of the well-known delta &lt;br&gt;method which is suitably adapted to handle smoothed empirical &lt;br&gt;processes.","abstract_has_math":false,"creators":["Gerds, Thomas"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Schumacher, Martin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:21:52Z","subjects":["Brier score","Überlebenszeitanalyse","efficient estimation","censored data","prediction error","survival analysis"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/702","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schumacher, Martin"]},{"key":"dc:creator","label":"Author","values":["Gerds, Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Brier score","Überlebenszeitanalyse","efficient estimation","censored data","prediction error","survival analysis"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Nonparametric efficient estimation of prediction error for incomplete data models","Nichtparametrisches, effizientes Schätzen des Vorhersagefehlers bei zensierten Daten"]}]}],"canonical_facts":{"dc:contributor":["Schumacher, Martin"],"dc:creator":["Gerds, Thomas"],"dc:description.abstract":["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."],"dc:format.medium":["application/pdf"],"dc:subject":["Brier score","Überlebenszeitanalyse","efficient estimation","censored data","prediction error","survival analysis"],"dc:title":["Nonparametric efficient estimation of prediction error for incomplete data models","Nichtparametrisches, effizientes Schätzen des Vorhersagefehlers bei zensierten Daten"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:52Z"}