Incorporating the Stochastic Process Setup in Parameter Estimation
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Estimation problems within the context of stochastic processes are usually studied with the help of statistical asymptotic theory and proposed estimators are tested with the use of simulated data. For processes with stationary increments it is customary to use differenced time series, treating them as selections from the increments’ distribution. Though distributionally correct, this approach throws away most information related to the stochastic process setup. In this paper we consider the above problems with reference to parameter estimation of a gamma process. Using the derived bridge processes we propose estimators whose properties we investigate in contrast to the gamma-increments MLE. The proposed estimators have a smaller bias, comparable variance and offer a look at the time-evolution of the parameter estimation. Empirical results are presented.
KeywordsLevy processes Gamma process Bridge process Dirichlet distribution
Mathematics Subject Classifications (2010)60G51 62F30
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