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Nonparametric detection with autoregressive data

The effects of autoregressive dependence on nonparametric detection are studied. An approximation technique is used to prove the asymptotic normality of a class of two-sample rank test statistics operating on stationary autoregressive processes. The effect of second-order autoregressive dependence on the asymptotic relative efficiency of the Mann-Whitney detector is illustrated. "Studentization" is proposed as a means of restoring the distribution-free character of rank tests when operating on dependent data. Under autoregressive dependence a consistent estimator for the variance of a class of two-sample rank test statistics is developed, and it is shown that the studentized versions of these statistics are asymptotically normal with mean zero and variance one. Simulation results are presented for the rate of convergence of the studentized two-sample Wilcox0n detector when operating on first-order and second-order stationary autoregressive processes.