The effect of autoregressive dependence on a nonparametric test (Corresp.)

The sign test, which is nonparametric when used on independent data, is shown to lose its distribution-free property on data of the form , where 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 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.