Analysis of outlier influence on nonlinear filter output for linearly increasing/decreasing signals with noise

The influence of an outlier present in a scanning window on nonlinear filter output characteristics like bias and variance is analyzed using output distributional influence functions and estimates of statistical parameters by computer simulation. The standard median, Wilcoxon and a-trimmed filters with different scanning window sizes are considered. The peculiarity of signal model is that besides constant signals we exploit the linearly increasing/decreasing ones. It is shown that there exist specific peculiarities of filter output behavior depending upon noise variance, outlier and signal derivative signs and values. Filter output bias and variance also depend on filter type and scanning window size. All these effects should be taken into account in many practical applications.