  In this paper, we investigate the linearity versus non-linearity of the Large
Magellanic Cloud (LMC) Cepheid period-luminosity (P-L) relation using two
statistical approaches not previously applied to this problem: the testimator
method and the Schwarz Information Criterion (SIC). The testimator method is
extended to multiple stages for the first time, shown to be unbiased and the
variance of the estimated slope can be proved to be smaller than the standard
slope estimated from linear regression theory. The Schwarz Information
Criterion (also known as the Bayesian Information Criterion) is more
conservative than the Akaike Information Criterion and tends to choose lower
order models. By using simulated data sets, we verify that these statistical
techniques can be used to detect intrinsically linear and/or non-linear P-L
relations. These methods are then applied to independent LMC Cepheid data sets
from the OGLE project and the MACHO project, respectively. Our results imply
that there is a change of slope in longer period ranges for all of the data
sets. This strongly supports previous results, obtained from independent
statistical tests, that the observed LMC P-L relation is non-linear with a
break period at/around 10 days.
