  We present a maximum-likelihood method for parameter estimation in terahertz
time-domain spectroscopy. We derive the likelihood function for a parameterized
frequency response function, given a pair of time-domain waveforms with known
time-dependent noise amplitudes. The method provides parameter estimates that
are superior to other commonly-used methods, and provides a reliable measure of
the goodness of fit. We also develop a simple noise model that is parameterized
by three dominant sources, and derive the likelihood function for their
amplitudes in terms of a set of repeated waveform measurements. We demonstrate
the method with applications to material characterization.
