Modelling stochastic time delay for regression analysis

TL;DR

This paper introduces a maximum likelihood regression model that accounts for stochastic time delays, improving prediction accuracy in systems where delays cause irregularities and noise.

Contribution

It proposes a novel approach to model stochastic time delays as errors, enhancing regression performance over traditional methods in certain scenarios.

Findings

Significant improvement over OLS regression in simulated univariate problems.

Effective handling of irregular alignments caused by stochastic delays.

Demonstrated advantages of the proposed model through simulation experiments.

Abstract

Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these challenges, we introduce a maximum likelihood regression model that regards stochastic time delay as an "error" in the time domain. For a certain subset of problems, by modelling both prediction and time errors it is possible to outperform traditional models. Through a simulated experiment of a univariate problem, we demonstrate results that significantly improve upon Ordinary Least Squares (OLS) regression.