Inference for Hidden Markov Models and related Models

Hidden Markov models (HMMs) and other latent variable models form complex, flexible frameworks for univariate and multivariate data structures. In the last two decades models with latent variables have entered almost all fields of statistical applications. It is common for these models that unobserved variables are introduced to model a complex data structure given by the observables. A major advantage of latent structures is the principle simplicity and the accessibility to practitioners as well as their application-driven interpretations rather than black box systems. In this dissertation the statistical methodology of HMMs and related models is extended in certain aspects and illustrated by several applications from various fields, including epileptic seizures, financial time series and a dental health trail. We first investigate testing problems for HMMs under nonstandard conditions, namely when the true parameter lies on the boundary. In practical applications of HMMs, non-standard testing problems are frequently encountered, e.g. testing for the probability of staying in a certain unobserved state being zero. We derive the relevant asymptotic distribution theory for the likelihood ratio test in HMMs under these conditions. A number of examples with particular relevance in the HMM framework are examined.