In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential nonparametric kernel procedures under local nonparametric...

An important problem of the statistical analysis of time series is to detect change-points in the mean structure. Since this problem is a one-dimensional version of the higher dimensional problem of detecting edges in images, we study detection rules which benefit from results obtained in image...

Motivated by applications in statistical quality control and signal analysis, we propose a sequential detection procedure which is designed to detect structural changes, in particular jumps, immediately. This is achieved by modifying a median filter by appropriate kernel-based jump preserving...

In this paper, sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its associated sequential partial sum process under...