title: Inference on the marginal distribution of clustered data with informative cluster size.
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.
authors: Department of Mathematics and Statistics, University of Turku, FI-20014 Turku, Finland.
authors: Jaakko
authors: J
authors: Nevalainen
authors: University of Louisville, Louisville, USA.
authors: Somnath
authors: S
authors: Datta
authors: University of Tampere, Tampere, Finland.
authors: Hannu
authors: H
authors: Oja
keywords: Clustered data; Informative cluster size; Marginal inference; Nonparametric models; Robustness