The estimation of in the firstorder autoregressive model: A Bayesian Approach
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Three general approaches to derive marginal posterior probability density functions for the autocorrelation coefficient of the firstorder normal autoregressive model are presented, from which Bayes estimators can be obtained for a given loss function. The different approaches are based on varying assumptions about the incidental parameters of the model and are shown numerically to be approximately equivalent with respect to their mean and variance. A comparison is made between the Bayes estimator and some classical estimators on the basis of the risk function and the expected risk. The risk functions are determined by Monte Carlo methods for quadratic, symmetric linear, and various asymmetric linear loss functions. The Bayes estimators are shown to be considerably advantageous, especially when the sample size is small. The Bayes estimators are also shown to be extremely robust under changes of the loss function. Copyright 1974 by the American Geophysical Union.
