On improved estimation in a conditionally Gaussian regression

TL;DR

This paper addresses improved methods for estimating the mean vector in a multivariate conditionally Gaussian setting, especially relevant for complex regression models involving Ornstein-Uhlenbeck processes with mixed noise components.

Contribution

It introduces novel estimation techniques tailored for conditionally Gaussian models with non-Gaussian components, enhancing accuracy in such complex regression scenarios.

Findings

Enhanced estimation accuracy demonstrated in simulations

Applicable to models with mixed Gaussian and non-Gaussian noise

Provides theoretical bounds for estimation performance

Abstract

The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time regression model with a non-Gaussian Ornstein--Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process.