### A comparison of three optimality criteria for observation channels

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The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....

We study the one-sided testing problem for the exponential distribution via the empirical Bayes (EB) approach. Under a weighted linear loss function, a Bayes test is established. Using the past samples, we construct an EB test and exhibit its optimal rate of convergence. When the past samples are not directly observable, we work out an EB test by using the deconvolution kernel method and obtain its asymptotic optimality.