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In data science applications such as ozone sensor monitoring computations and analysis of the covariance matrix often has to be done in a low-sample-size-high-dimensional (LSHD) regime. We present recent results on LSHD asymptotics for bilinear forms of the sample covariance matrix. The theoretical results hold without the need to constraint the dimension relative to the sample size. This approach allows to detect and infer changes in the dependence structure. To estimate unknowns, we propose and study in-sample estimators, which avoid a learning sample. Simulations show that the proposed methods work reliable for realistic models.
?As a real world application the method is applied to analyze monitoring data from ozone sensors. The sensor data is compressed by projecting it onto sparse principal directions obtained by a sparse principal component analysis (SPCA). It turns out that the SPCA automatically learns the spatial locations of the sensors and leads to a spatial segmentation. Analyzing the projections for a change-point provides a mean to detect changes in the spatial dependence structure of the sensor network measuring ozone.
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