The application of estimation theory for predicting peak ground motion is critically examined in order to be more precise in its application. Estimation theory relates peak ground motion to the duration and spectrum of the signal. Using vertical component data from the Eastern Canada Telemetered Network, at distance range of 100–1000 km, we find that a duration must be defined by the interval where the cumulative energy of the main signal increases linearly, here between 5% and 75% of the cumulative power. This duration, when used with the spectra within this window, adequately replicates observed peak motions. This duration used differs significantly from that used by Herrmann (1985) and Toro and McGuire (1987) beyond 500 km. The estimation theory is extended to estimate confidence limits on the peak motion. Finally, the relation between various spectral level estimators, linear, logarithmic, and RMS, is considered to point out the need for consistency in spectral level estimation using smooth models.