  Wind-generated waves are often treated as stochastic processes. There is
particular interest in their spectral density functions, which are often
expressed in some parametric form. Such spectral density functions are used as
inputs when modelling structural response or other engineering concerns.
Therefore, accurate and precise recovery of the parameters of such a form, from
observed wave records, is important. Current techniques are known to struggle
with recovering certain parameters, especially the peak enhancement factor and
spectral tail decay. We introduce an approach from the statistical literature,
known as the de-biased Whittle likelihood, and address some practical concerns
regarding its implementation in the context of wind-generated waves. We
demonstrate, through numerical simulation, that the de-biased Whittle
likelihood outperforms current techniques, such as least squares fitting, both
in terms of accuracy and precision of the recovered parameters. We also provide
a method for estimating the uncertainty of parameter estimates. We perform an
example analysis on a data-set recorded off the coast of New Zealand, to
illustrate some of the extra practical concerns that arise when estimating the
parameters of spectra from observed data.
