On statistical estimation and inferences in optional regression models

摘要

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well known that statistical data may present an information flow/filtration without 'usual conditions'. The estimation problem is achieved by means of structural least squares (LS) estimates and their sequential versions. The main results of the paper are devoted to the strong consistency of such LS-estimates. For sequential LS-estimates, the property of fixed accuracy is proved. Finally, several illustrative examples from risk theory and mathematical finance are presented.