Improved estimation in a non-Gaussian parametric regression

TL;DR

This paper develops improved estimation methods for parameters in a non-Gaussian continuous-time regression model with pulse noise, using a modified James-Stein approach that outperforms least squares estimates.

Contribution

It introduces a novel estimation scheme based on a modified James-Stein procedure for non-Gaussian noise, reducing quadratic risk in parameter estimation.

Findings

Proposed estimators have smaller quadratic risk than least squares.

Method effectively handles non-Gaussian pulse noise.

Applicable to discrete-time models with autoregressive noise.

Abstract

The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The noise is specified by the Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James-Stein procedure with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.