Investigations of the Non-Linear LMC Cepheid Period-Luminosity Relation with Testimator and Schwarz Information Criterion Methods

摘要

In this paper, we investigate the linearity versus non-linearity of the LargeMagellanic Cloud (LMC) Cepheid period-luminosity (P-L) relation using twostatistical approaches not previously applied to this problem: the testimatormethod and the Schwarz Information Criterion (SIC). The testimator method isextended to multiple stages for the first time, shown to be unbiased and thevariance of the estimated slope can be proved to be smaller than the standardslope estimated from linear regression theory. The Schwarz InformationCriterion (also known as the Bayesian Information Criterion) is moreconservative than the Akaike Information Criterion and tends to choose lowerorder models. By using simulated data sets, we verify that these statisticaltechniques can be used to detect intrinsically linear and/or non-linear P-Lrelations. These methods are then applied to independent LMC Cepheid data setsfrom the OGLE project and the MACHO project, respectively. Our results implythat there is a change of slope in longer period ranges for all of the datasets. This strongly supports previous results, obtained from independentstatistical tests, that the observed LMC P-L relation is non-linear with abreak period at/around 10 days.