On Efficiency and Exponential Families in Stochastic Process Estimation
A general definition of efficiency for stochastic process estimation is proposed and some of its ramifications are explored. Of particular importance in the definition is the form of the derivative of the logarithm of the likelihood. The question of the simplest possible form for this leads on to a discussion of extensions of the concepts of sufficiency and exponential families, the latter in a Markov process context. The paper concludes with several illustrative examples.
Key WordsStochastic process estimation efficiency sufficiency exponential family maximum likelihood Martingale limit theory branching process first order autoregression power series distributions
Unable to display preview. Download preview PDF.