  A significant problem with most functional data analyses is that of
misaligned curves. Without adjustment, even an analysis as simple as estimation
of the mean will fail. One common method to synchronize a set of curves
involves equating ``landmarks'' such as peaks or troughs. The landmarks method
can work well but will fail if marker events can not be identified or are
missing from some curves. An alternative approach, the ``continuous monotone
registration'' method, works by transforming the curves so that they are as
close as possible to a target function. This method can also perform well but
is highly dependent on identifying an accurate target function. We develop an
alignment method based on equating the ``moments'' of a given set of curves.
These moments are intended to capture the locations of important features which
may represent local behavior, such as maximums and minimums, or more global
characteristics, such as the slope of the curve averaged over time. Our method
works by equating the moments of the curves while also shrinking toward a
common shape. This allows us to capture the advantages of both the landmark and
continuous monotone registration approaches. The method is illustrated on
several data sets and a simulation study is performed.
