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.

When white noise generated by an underlying Poisson process is filtered by any member of a large class of stable (not necessarily linear nor stationary) filters, the first-order probability distributions of the filter output is infinitely divisible. The Kolmogorov canonical form for the characteristic function is displayed and related to the parameters of the white noise and of the filter. In certain linear stationary cases, cubclasses of the infinitely divisible distributions are identified. An invariance property of the bilateral exponential distribution is demonstrated.

The sign test, which is nonparametric when used on independent data, is shown to lose its distribution-free property on data of the formX_{t}= \varrho X_{t-1} + W_{t}, 0 < |\varrho | < 1, where\{W_{t}\}is a sequence of independent and identically distributed random variables. Asymptotic normality of the sign-test statistic is proved in two cases. If the data\{X_{t}are regarded as regularly spaced samples of a continuous-parameter lowpass process, then upon increasing the sampling rate indefinitely, the continuous-time sign test, an infinite clipper followed by an integrator, is also not distribution-free.

The least mean square error predictor is shown to be linear for a class of processes that are generated by passing independent white noise through a minimum-phase linear filter. Many random processes generated in this way are non-Gaussian.

It is shown that the polarity-coincidence correlator (PCC), a two-input detection device, is nonparametric in its false-alarm rate with respect to a wide class of signal and noise distributions. Operating in fixed distributions, the probability of detection is a nondecreasing function of input SNR. Although the PCC performs less well than an ordinary correlator or a Neyman-Pearson detector for Gaussian inputs, it can be markedly superior to both.