Jackknifing multitaper spectrum estimates

Abstract

This article has summarized some theory on multitaper estimates, the jackknife, and their use together, and given some examples where the jackknife indicates problems with the basic estimate. These examples all use jackknifing over windows, as opposed to exchanging data blocks or residuals from parametric models. Indeed, in most of the problems I have encountered, spectra with both large ranges and many line components appear to be the rule rather than the exception, and it is not clear how any other method could work. In spectrum estimation problems, the jackknife is rarely an end in itself, but when studying scientific and engineering data where the basic inferences depend on having accurate estimates of spectra or descriptions of the data under study, it is an invaluable diagnostic of possible problems. In such problems, one rarely cares if a particular statistic is significant at the 94% or 96% level, but a variance estimate that is ten or 100 times too large or too small requires serious attention. Thus, when the jackknife variance has a suspicious average or is either extremely low or extremely high at some frequencies, exploratory data analysis is mandatory. © 2007 IEEE.