Statistical Dictionary of Terms and Symbols

Any device being used to record a time series has a natural maximum reading frequency which it is impossible or impractical to exceed, and this limits the absolute frequency range over which a spectrum estimate may be made. It is shown that if one may use two such devices, which do not have the same sampling period, to measure the the same process, then spectrum estimates may be made over a wider absolute frequency range than would normally be possible. Upper bounds to the asymptotic variance of such estimates are calculated and discussed.

The situation is treated as a particular type of missing data problem, and part of the work presented here applies to a larger class of missing data problems (those with periodic amplitude modulating function.)