A Limit Theory for Likelihood Ratio Test under Unidentifiability
for General Dependent Processes

 Yuewu Xu
Fordham University


        In many important practical hypothesis testing problems about substructures of the population, the regularity conditions of the classical likelihood ratio test theory fail to hold, due to a lack of identifiability of the parameters under the null hypothesis and other serious violations. Under mild regularity conditions, this paper establishes the limit theory for the likelihood ratio tests under unidentiability for general dependent  processes.  Practical applications include testing for the number of components in mixture models, testing for the order of ARMA models, testing for the order of Hidden Markov Models, etc.

Co-authors: Yongzhao Shao, New York University