Effective nonparametric estimation in the case of severely discretized data |
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| Affiliation: | 1. Institute of Transfusion Medicine and Immunology, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, German Red Cross Blood Donor Service Baden-Württemberg—Hessen, Institute Mannheim, Germany;2. Endocrinology Department, 5th Medical Department, Medical Faculty Mannheim, Heidelberg University Mannheim, Baden-Württemberg, Germany;3. Flow Core Mannheim, Medical Faculty Mannheim, Heidelberg University, Mannheim, Baden-Württemberg, Germany;1. Department of Hyperbaric and Intensive Care Medicine, Alfred Health, Melbourne, Australia;2. Trauma Service, Alfred Health, Melbourne, Australia;3. National Trauma Research Institute, Melbourne, Australia;4. Australian and New Zealand Intensive Care Research Centre, Monash University, Melbourne, Australia;1. Population Health Office - Directorate of Research, Study, Evaluation and Statistics (DREES) – Health Ministry, Paris, France;2. Department of Medical Information - University Hospital (CHRU), Nancy, France;3. Université de Paris, CRESS, Obstetrical Perinatal and Pediatric Epidemiology Research Team, EPOPé, INSERM, INRA, Paris, France;4. Program in Public Health & Center for Population, Inequality and Policy, University of California, Irvine, Irvine, CA;5. Assistance Publique - Hôpitaux de Paris, Clinical Investigation Center, Paris, France |
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| Abstract: | Often economic data are discretized or rounded to some extent. This paper proposes a regression and a density estimator that work especially well when discretization causes conventional kernel-based estimators to behave poorly. The estimator proposed here is a weighted average of neighboring frequency estimators, and the weights are composed of cubic B-splines. Interestingly, we show that this estimator can have both a smaller bias and variance than frequency estimators. As a means to obtain asymptotic normality and rates of convergence, we assume that the discreteness becomes finer as the sample size increases. |
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