用T估计和Schwarz信息准则研究造父变星周期-光度关系的非线性LMC
Investigations of the Non-Linear LMC Cepheid Period-Luminosity Relation with Testimator and Schwarz Information Criterion Methods
摘要：
在本文中，我们研究的线性和非线性的大麦云（LMC）造父变星的周期光度（P-L）的关系，使用两种统计方法以前没有应用到这个问题：testimetry方法和施瓦茨信息准则（SIC）。首次将该方法推广到多阶段，证明了该方法是无偏的，且估计斜率的方差小于线性回归理论估计的标准斜率。施瓦茨信息准则（也称为贝叶斯信息准则）比赤池信息准则更保守，倾向于选择低阶模型。通过使用模拟数据集，我们验证了这些统计技术可以用来检测内在的线性和/或非线性的P-L关系。这些方法，然后应用到独立的LMC造父变星数据集的OGLE项目和OOO项目，分别。我们的结果意味着，有一个变化的斜率在较长的周期范围内的所有数据集。这强烈支持先前的结果，从独立的统计检验，观察到的LMC P-L关系是非线性的，在/约10天的中断期。
英文摘要：
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.
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