Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Research Unit 1735

Semiparametric approach to structural adaptive estimation

Most statistical problems in high dimension are too complex to be solved without any additional information about the structure of the model. Often this information can be described in a semiparametric form: the target representing the informative part of the model is described by a relatively low-dimensional parameter, while the whole model description involves a potentially high-dimensional nuisance parameter. Typical examples are built by the problems of dimensionality reduction: the observed data are high dimensional but the underlying structural assumption is that the whole dataset can be projected onto the low dimensional subspace without significant loss of important information. The problem of adaptive estimation includes recovering the underlying structure from the data which is further used for the inference about the model. The main question under consideration is whether the target structural parameter can be efficiently estimated under the presence of a high dimensional nuisance. The profile maximum likelihood approach based on the global optimisation of the log-likelihood, in spite of its nice theoretical properties, leads to a complex (unfeasible), non-convex, high-dimensional optimisation problem. This optimisation is usually replaced by sequential alternating optimisation leading to iterative EM-type methods. The overall quality of such iterative procedures is only addressed for some rather special situations. Within this project we aim to address the problem of accuracy and efficiency of such statistical procedures within the unified semiparametric framework. The special focus is on the range of applicability of each method and especially on the critical dimension of the target and nuisance parameters. The obtained results will be applied to the problems of high dimensional classification and clustering from medical imaging and pharmakinetics.


The principal investigators are


Scientific staff is