  We develop two algorithms, based on maximum likelihood (ML) inference, for
estimating the parameters of polarized radio sources which emit at a single
rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux
density spectrum of the source, either a power law or a scaled version of the
Stokes I spectrum, and a variation in sensitivity across the observing band. We
quantify the detection significance and measurement uncertainties in the fitted
parameters, and we derive weighted versions of the RM synthesis algorithm
which, under certain conditions, maximize the likelihood. We use Monte Carlo
simulations to compare injected and recovered source parameters for a range of
signal-to-noise ratios, investigate the quality of standard methods for
estimating measurement uncertainties, and search for statistical biases. These
simulations consider one frequency band each for the Australia Telescope
Compact Array (ATCA), the Square Kilometre Array (SKA), and the Low Frequency
Array (LOFAR). We find that results obtained for one frequency band cannot be
easily generalized, and that methods which were developed in the past for
correcting bias in individual frequency channels do not apply to wide-band data
sets. The standard method for estimating the measurement uncertainty in RM is
not accurate for sources with non-zero spectral indices. Furthermore, dividing
Stokes Q and U by Stokes I to correct for spectral index effects, in
combination with RM synthesis, does not maximize the likelihood.
