On statistical estimation and inferences in optional regression models

TL;DR

This paper investigates estimation methods for a broad class of optional regression models involving optional semimartingales, establishing strong consistency and fixed accuracy of least squares estimates in complex information flow settings.

Contribution

It introduces and analyzes least squares estimation techniques for optional semimartingale models, proving their strong consistency and fixed accuracy without usual filtration conditions.

Findings

Strong consistency of LS-estimates in optional regression models

Sequential LS-estimates achieve fixed accuracy

Applicable to models with complex information flows

Abstract

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.