The minimum mean square estimator for a sublinear operator

TL;DR

This paper investigates the properties of the minimum mean square estimator for sublinear operators, establishing existence, uniqueness, and characterizations, and linking it to risk measures and g-expectations.

Contribution

It introduces new theoretical results on the minimum mean square estimator for sublinear operators, including existence, uniqueness, and its relation to risk measures.

Findings

Proves existence and uniqueness of the estimator under mild conditions

Provides multiple characterizations of the estimator

Explores connections with risk measures and g-expectations

Abstract

In this paper, we study the minimum mean square estimator for a sublinear operator. Under some mild assumptions, we prove the existence and uniqueness of the minimum mean square estimator. Several characterizations of the minimum mean square estimator are obtained. We also explore the relationship between the minimum mean square estimator and the conditional coherent risk measure and conditional g-expectation.