Nonparametric Changepoint Estimation for Sequential Nonlinear Profile Monitoring

We consider changepoint detection in a process in which the observed points are profiles: large sets of functionally related points (x,y). Few changepoint detection methods have been proposed that do not rely in some capacity on the assumption that the observational errors are normally distributed. In this paper, a nonparametric distribution‐free wavelet method is proposed for monitoring for changes in sequences of nonlinear profiles. No assumptions are made on the nature or form of the changes between the profiles other than finite square‐integrability, and no distributional assumption is made on the noise. Using only the magnitudes and location maps of thresholded wavelet coefficients, our method uses the spatial adaptivity property of wavelets to accurately detect profile changes when the signal is obscured with a variety of non‐Gaussian errors. The proposed method outperforms existing (and much more complex) methods under various conditions of non‐Gaussianity. The method does not rely on estimates designed for normally distributed errors, yet it is robust enough to work reasonably well under Gaussian conditions. The efficiency of the proposed method, including comparisons with existing profile monitoring methods, is shown via simulation. We also apply the proposed method to vertical density profile data, a common real data set used in profile monitoring.