  A number of recent works have suggested that the period-luminosity (PL)
relation for the Large Magellanic Cloud (LMC) Cepheids exhibits a controversial
nonlinear feature with a break period at 10 days. Therefore, the aim of this
Research Note is to test the linearity/nonlinearity of the PL relations for the
LMC Cepheids in BVIcJHKs band, as well as in the Wesenheit functions. We show
that simply comparing the long and short period slopes, together with their
associate d standard deviations, leads to a strictly larger error rate than
applying rigorous statistical tests such as the F-test. We applied various
statistical tests to the current published LMC Cepheid data. These statistical
tests include the F-test, the testimator test, and the Schwarz information
criterion (SIC) method. The results from these statistical tests strongly
suggest that the LMC PL relation is nonlinear in BVIcJH band but linear in the
Ks band and in the Wesenheit functions. Using the properties of period-color
relations at maximum light and multi-phase relations, we believe that the
nonlinear PL relation is not caused by extinction errors.
