Abstract: multi-taper methods aim to recover the spectral density of a point process by weighting the data with different masks and then performing an average that reduces variance. I'll present performance bounds for one central example of those methods: Thomson's spectral estimator. The estimates allow us to quantify the trade-off between bias and variance reduction. The key element of the analysis is thedescription of the aggregated profile of the data tapers. I'll discuss other applications of these methods in time-frequency analysis and determinantal point processes.
This is joint work with Luis Daniel Abreu - Acoustics Research Institute, Austrian Academy of Sciences.