The Cepheid Period-Luminosity (PL) relation is crucial to establish the size scale of the Universe independent of the Cosmic Microwave Background. A greater understanding of its systematics and underlying physics is therefore vital. Here we adapt the testimator approach, previously used to study a possible nonlinearity in the slope of the PL relation, to look at possible variations in the dispersion of the PL relation as a function of period-or heteroskedasticity. We describe the mathematics behind our new test and some test calculations. We then apply it to Large Magellanic Cloud Cepheid PL data using published reddenings, and show that there is a reduction in the variance of the PL relation around 10 days. While this could be due to errors in reddenings, analysis of multiphase PL relations suggest that this is a real feature. We close with a discussion of the possible implications of this result for the extra-galactic distance scale and stellar pulsation.
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