Download Hidden Markov and other models for discrete-valued time by Iain L. MacDonald, Walter Zucchini PDF

By Iain L. MacDonald, Walter Zucchini

This booklet describes quite a few hidden Markov types and issues out the place they come up and the way to estimate parameters of the version. It additionally issues out the place they come up in a average demeanour and the way the versions can be utilized in functions. it's not imagined to be a mathematically rigorous remedy of the topic for which one should still glance somewhere else just like the e-book via R.J.Elliott, L.Aggoun and J.B.Moore (1995): Hidden Markov versions: Estimation and keep an eye on. Springer-Verlag. you'll be able to learn. however it lacks intensity to a definite volume and isn't finished sufficient to fulfill all forms of wishes.

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Additional resources for Hidden Markov and other models for discrete-valued time series

Example text

Taking P(SI = 1) to be B1 completes the specification of the process: SI, S2, ... , ST is then a binary (nonhomogeneous) Markov chain with E(St) - Bt for all t, arid with the odds ratio for (St-I, St) in all cases equal to 'ljJ. For a series of observations 81, S2, ... 3) for t > 1,and IPso taken to be (}l. ) Maximization of this likeli-:hood has to be performed numerically. Although Azzalini gives the first derivatives, he states that it does not seem feasible to obtain , expressions for the second-order derivatives.

An application to health-care utilization by 300 families enrolled in a health-maintenance plan in Maryland is described. The second paper cited above refers to situations (and models) in which the vector of responses may include both discrete and continuous components. For each response some link function of the conditional mean is taken to be linear in the current covariates, the current values of the other responses, and the past values 8£ all the responses. i of the conditional mean. The approach already described,based on the quasi-likelihood 'estimating equa,tions', rriay be generalized to provide an estimate of the vector of parameters.

Raftery proves the following limit theorem, on the assumption that the elelnents of Q are positive: if 1f is the stationary distribution corresponding to Q, St == j has limiting probability 1fj independent of the initial conditions. That is, limP(St ==j I Sl -iI," .. ,Sz ==iz) == t-+CXJ 1fj for all j, i l , ... ,izE M. It is therefore reasonable to restrict one's consideration to stationary mode~s {St}. g. Brockwell and Davis, 1991, p. 239). == 0, we have for kEN l P(k) == LAgP(k - g)Q. 5) g=l It is not always possible to solve these equations uniquely, .

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