Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes

TL;DR

This paper demonstrates that for partially observed multiscale diffusion models, the filtering process can be reduced in dimension, enabling more efficient statistical estimation of unknown parameters without losing accuracy.

Contribution

It establishes a general theoretical framework showing filter convergence to a lower-dimensional form, facilitating parameter estimation in complex multiscale systems.

Findings

Filter of the original model converges to a reduced dimension filter

Reduced-dimension models enable effective parameter estimation

Simulation results support theoretical convergence and estimation accuracy

Abstract

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.