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Inference on the marginal distribution of clustered data with informative cluster size
Jaakko Nevalainen1, Somnath Datta2, Hannu Oja3
1Department of Mathematics and Statistics, University of Turku, FI-20014 Turku, Finland.
Abstract:
In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating mechanisms, parametric and nonparametric models are considered in light of examples. Our emphasis is on nonparametric and robust approaches to the inference on the marginal distribution. Descriptive statistics and parameters of interest are defined as functionals and they are accompanied with a generally applicable testing procedure. The theory is illustrated with an example on patients with incomplete spinal cord injuries.
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