Dual Estimation in State Space Models with Violation to Normality: A Comparison between the Extended Kalman Filter and the Particle Filter
Open Access
Author:
Chen, Meng
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
November 15, 2019
Committee Members:
Murali Haran, Thesis Advisor/Co-Advisor Le Bao, Committee Member Ephraim Mont Hanks, Committee Member Ephraim Mont Hanks, Program Head/Chair
Keywords:
state space model Kalman filter particle filter dual estimation
Abstract:
In the field of psychology and developmental science, researchers often study the change of some underlying latent construct over time. It is of interest both to estimate the latent states that an individual is in and to extract patterns that would characterize the change process. Translated into dynamic modeling language, researchers are interested in the dual estimation of states and model parameters. Filtering methods, such as the commonly adopted Kalman filter, can aid in this process. However, when the linear and normality assumptions of the Kalman filter is challenged, the estimates may no longer be reliable. This thesis set out to investigate how one algorithm from the Kalman filter family, the extended Kalman filter (EKF), and an alternative, simulation-based approach of particle filter, behave under the ideal condition of normality and when the normality assumption is violated, through a set of simulations. Results from simulations show, for both algorithms, overall satisfactory performance under the ideal normal condition, and frequently biased parameter estimates when the distribution of process noises was skewed. The particle-filter-associated approach slightly outperforms the EKF-associated approach when the optimization problem becomes harder. Caveats regarding the interpretation of results are discussed along with potential future research directions.
