A nonparametric signal detector for trend with dependent input data

Abstract The input data of classical nonparametric signal detectors must be independent. Kassam and Thomas [1] consider a class of non-parametric detectors with statistically dependent input data for detecting a d c -signal in the presence of additive noise. However, in many signal detection problems, the signal is not constant but is an increasing function of time. For statistically independent input data Cox and Stuart [2] developed a non-parametric test against trend which can be implemented very easily with modern integrated circuits. This trend test can be modified easily by the scheme of Kassam and Thomas. In this paper the asymptotic relative processing time (ARPT) of the modified Cox-Stuart detector has been calculated with respect to the unmodified Cox-Stuart detector, the best parametric detector (for Gaussian noise based on the sample regression coefficient) and the Kendall-τ detector. These calculations have been made for noise processes with known autocorrelation function and with Gaussian, uniform, Laplace or exponential univariate probability density function.