Parameter estimation for a two-state semi-Markov model of a univariate point process.
Hornback, James Leroy
Lewis, Peter A.W.
Thomas, Marlin U.
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Using the convenient second-order interval properties of a two-state semi-Markov model for a univariate point process, an automated technique for the estimation of the parameters in the model was researched and discussed. The power spectral density of intervals was estimated by the periodogram and a Kolmogorov-Smirnov test of fit was conducted. The asymtotic exponential distribution and independence of the periodogram points were used to calculate an approximate likelihood function. A system of equations was then formed to find the maximum likelihood estimates of the parameters. Since closed-form solutions for the estimates could not be found, an iterative method to stabilize initial guesses of the parameter values was attempted with only limited success. Results on using Kolmogorov-Smirnov type statistics and the spectrum of intervals to test the fit of stochastic process models to data have also been obtained.
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