|M.Sc Student||Noemie Sellam Balouka|
|Subject||Simultaneous Confidence Bands for a Multivariate|
|Department||Department of Industrial Engineering and Management||Supervisor||Assistant Professor Nardi Yuval|
|Full Thesis text|
We propose a method for constructing simultaneous confidence bands for a multivariate spectral density of a stationary process. The construction of these bands is pivoted on a nonparametric spectral estimator, a smoothed version of the periodogram. We show that this problem may be reduced to finding the probability that the maxima of a certain non-Gaussian random field exceeds a given threshold. We adapt earlier results in the literature about tail probabilities of maxima of random fields to the problem in hand, and present a general result about the distribution of the maxima of the standardized nonparametric spectral estimator. We then show how this result may be used to construct the required confidence bands. Finally, we present several simulation results.