The estimation of the ratio of two density probability functions is of great interest in many statistics fields, including causal inference. In this study, we develop an ensemble estimator of density ratios with a novel loss function based on super learning. We show that this novel loss function is qualified for building super learners. Two simulations corresponding to mediation analysis and longitudinal modified treatment policy in causal inference, where density ratios are nuisance parameters, are conducted to show our density ratio super learner's performance empirically.
Practical considerations for variable screening in the super learner
Biostatistics Division, Kaiser Permanente Washington Health Research Institute（Kaiser Permanente华盛顿健康研究机构生物统计学部）；Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center（弗雷德 Hutchinson癌症研究中心疫苗与传染病部）；Department of Biostatistics, University of Washington（华盛顿大学生物统计学系）；Seattle Central College（西雅图中央学院）
Bootstrap Bias Corrected Cross Validation applied to Super Learning
Computational Centre, University of Bialystok（比亚韦斯托克大学计算中心）；Institute of Informatics, University of Bialystok（比亚韦斯托克大学信息学院）；Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw（华沙大学跨学科数学与计算建模中心）
Department of Mathematics（数学系）；King’s College London（伦敦国王学院）；Department of Statistics and Operations Research（统计与运筹学系）；Department of Statistical Science（统计科学系）；University of Granada（格拉纳达大学）；University College London（伦敦大学学院）
