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Robust real-time monitoring of high-dimensional data streams has many important real-world applications such as industrial quality control, signal detection, biosurveillance, but unfortunately it is highly non-trivial to develop efficient schemes due to two challenges: (1) the unknown sparse number or subset of affected data streams and (2) the uncertainty of model specification for high-dimensional data. In this article, motivated by the detection of smaller persistent changes in the presence of larger transient outliers, we develop a family of efficient real-time robust detection schemes for high-dimensional data streams through monitoring feature spaces such as PCA or wavelet coefficients when the feature coefficients are from Tukey-Hubers gross error models with outliers. We propose to construct a new local detection statistic for each feature called $L_{alpha}$-CUSUM statistic that can reduce the effect of outliers by using the Box-Cox transformation of the likelihood function, and then raise a global alarm based upon the sum of the soft-thresholding transformation of these local $L_{alpha}$-CUSUM statistics so that to filter out unaffected features. In addition, we propose a new concept called false alarm breakdown point to measure the robustness of online monitoring schemes, and also characterize the breakdown point of our proposed schemes. Asymptotic analysis, extensive numerical simulations and case study of nonlinear profile monitoring are conducted to illustrate the robustness and usefulness of our proposed schemes.
In this article, motivated by biosurveillance and censoring sensor networks, we investigate the problem of distributed monitoring large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data stre
In many real-world problems of real-time monitoring high-dimensional streaming data, one wants to detect an undesired event or change quickly once it occurs, but under the sampling control constraint in the sense that one might be able to only observ
Structural breaks have been commonly seen in applications. Specifically for detection of change points in time, research gap still remains on the setting in ultra high dimension, where the covariates may bear spurious correlations. In this paper, we
For a multivariate linear model, Wilks likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, th
We propose a new method for changepoint estimation in partially-observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a MissCUSUM tra