ABSTRACT
This chapter explores the estimation of standard errors for parameters. The likelihood of hidden Markov models (HMM) is a complicated function of the parameters and frequently has several local maxima. The goal of course is to find the global maximum, but there is no simple method of determining in general whether a numerical maximization algorithm has reached the global maximum. The algorithm is easily modified to compute the log-likelihood without assuming stationarity of the Markov chain. Relatively little is known about the properties of the maximum likelihood estimators of HMMs; only asymptotic results are available. One can estimate the standard errors from the Hessian of the log-likelihood at the maximum, but this approach runs into difficulties when some of the parameters are on the boundary of their parameter space, which occurs quite often when HMMs are fitted.
