  In this paper, we analyze the structure of RRab star light curves using
Principal Component Analysis. We find this is a very efficient way to describe
many aspects of RRab light curve structure: in many cases, a Principal
Component fit with 9 parameters can describe a RRab light curve including bumps
whereas a 17 parameter Fourier fit is needed. As a consequence we show
statistically why the amplitude is also a good summary of the structure of a RR
Lyrae light curve. We also use our analysis to derive an empirical relation
relating absolute magnitude to light curve structure. In comparing this formula
to those derived from exactly the same dataset but using Fourier parameters, we
find that the Principal Component Analysis approach has disticnt advantages.
These advantages are, firstly, that the errors on the coefficients in such
formulae are smaller, and secondly, that the correlation between Principal
Components is significantly smaller than the correlation between Fourier
amplitudes. These two factors lead to reduced formal errors, in some cases
estimated to be a factor of 2, on the eventual fitted value of the absolute
magnitude. This technique will prove very useful in the analysis of data from
existing large scale survey projects concerning variable stars.
