Testing for two states in a hidden Markov model |
| |
Authors: | Jörn Dannemann Hajo Holzmann |
| |
Affiliation: | 1. Institute for Mathematical Stochastics, University of G?ttingen DE‐37077 G?ttingen, Germany;2. Institute for Stochastics, Karlsruhe University DE‐76128 Karlsruhe, Germany |
| |
Abstract: | The authors consider hidden Markov models (HMMs) whose latent process has m ≥ 2 states and whose state‐dependent distributions arise from a general one‐parameter family. They propose a test of the hypothesis m = 2. Their procedure is an extension to HMMs of the modified likelihood ratio statistic proposed by Chen, Chen & Kalbfleisch (2004) for testing two states in a finite mixture. The authors determine the asymptotic distribution of their test under the hypothesis m = 2 and investigate its finite‐sample properties in a simulation study. Their test is based on inference for the marginal mixture distribution of the HMM. In order to illustrate the additional difficulties due to the dependence structure of the HMM, they show how to test general regular hypotheses on the marginal mixture of HMMs via a quasi‐modified likelihood ratio. They also discuss two applications. |
| |
Keywords: | Finite mixture hidden Markov model likelihood ratio test marginal distribution maximum likelihood estimation Wald test |
|