Simultaneous confidence bands in spectral density estimation

We propose a method for the construction of simultaneous confidencebands for a smoothed version of the spectral density of a Gaussianprocess based on nonparametric kernel estimators obtained bysmoothing the periodogram. A studentized statistic is used todetermine the width of the band at each frequency and a frequency-domainbootstrap approach is employed to estimate the distributionof the supremum of this statistic over all frequencies. We proveby means of strong approximations that the bootstrap estimatesconsistently the distribution of the supremum deviation of interestand, consequently, that the proposed confidence bands achieveasymptotically the desired simultaneous coverage probability.The behaviour of our method in finite-sample situations is investigatedby simulations and a real-life data example demonstrates itsapplicability in time series analysis.     

Persistent Antibody Clonotypes Dominate the Serum Response to Influenza over Multiple Years and Repeated Vaccinations

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