A Self-Normalized Online Monitoring Method Based on the Characteristic Function

The goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an additional self-normalization factor, which enables effective control the Type I error. We theoretically investigate the asymptotic properties of the monitoring method under the null hypothesis as well as the alternative hypothesis. Since the asymptotic distribution under the null hypothesis is quite complicated, we apply the multivariate stationary bootstrap method to estimate the critical value of the sequential test. Numerical simulations and a real-world application demonstrate the usefulness of the proposed method.