טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSellam Balouka Noemie
SubjectSimultaneous Confidence Bands for a Multivariate
Spectral Density
DepartmentDepartment of Industrial Engineering and Management
Supervisor Assistant Professor Yuval Nardi
Full Thesis textFull thesis text - English Version


Abstract

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.