Open Collections

Zhou, Yining

University of British Columbia

The maximum likelihood estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality. However, the estimated transition probability matrix derived from MLE lacks accuracy compared to the real one, and LRT is inefficient in high-dimensional Markov chains. In this study, we extended the adaptive Lasso technique from linear models to Markov chains and proposed a novel model by applying penalized maximum likelihood estimation to optimize the estimation of the transition probability matrix. We name this novel methodology McALasso. Additionally, we demonstrated that McALasso enjoys oracle properties, meaning the estimated transition probability matrix performs as well as the true one when given. Simulations show that our new method performs very well overall in comparison with various competitors. Real data analysis further convinces us of the value of our proposed method.

Text

2024-09-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/89252

Mathematics

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/