Information Bounds and Nonparametric Maximum Likelihood Estimation

In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. This text provides an account of recent developments in the theory of nonparametric and semiparametric estimation. The first part deals with information lower bounds and differentiable functionals. The second part focuses on nonparametric maximum likelihood estimators for interval censoring and deconvolution. The distribution theory of these estimators is developed and new algorithms for computing them are introduced. The models apply frequently in biostatistics and epidemiology and, although they have been used as a data-analytic tool for a long time, their properties have been largely unknown.