Noncurved exponential families associated with observations over finite state Markov chains. (English) Zbl 0798.62096
Summary: We show that, contrary to earlier claims, for each ergodic and homogeneous finite-state Markov chain with either discrete or continuous time-parameter there are stopping times which have the property that they reduce the corresponding curved exponential families to noncurved exponential ones.
MSC:
62M99 | Inference from stochastic processes |
60G40 | Stopping times; optimal stopping problems; gambling theory |
60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
60J27 | Continuous-time Markov processes on discrete state spaces |