The effect of autoregressive dependence on a nonparametric test (Corresp.)
S. Wolff, Joseph L. Gastwirth, Herman Rubin · IEEE Transactions on Information Theory · 1967
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.