Investigations of the nonlinear LMC Cepheid period-luminosity relation with testimator and Schwarz Information Criterion methods

In this paper, we investigate the linearity versus nonlinearity 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 and is 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 prefer lower order models. By using simulated data sets, we verify that these statistical techniques can be used to detect intrinsically linear and nonlinear P-L relations. These methods are then applied to independent LMC Cepheid data sets from the OGLE and MACHO projects. 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, which show that the observed LMC P-L relation is nonlinear, with a break period at or around 10 days.