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We present the largest M31 near-infrared (F110W (close to J band), F160W (Hband)) Cepheid sample so far. The sample consists of 371 Cepheids withphotometry obtained from the HST PHAT program. The sample of 319 fundamentalmode Cepheids, 16 first overtone Cepheids and 36 type II Cepheids, wasidentified using the median absolute deviation (MAD) outlier rejection methodwe develop here. This method does not rely on priors and allows us to obtainthis clean Cepheid sample without rejecting a large fraction of Cepheids. Theobtained Period-Luminosity relations (PLRs) have a very small dispersion, i.e.0.155 mag in F160W, despite using random phased observations. This remarkablysmall dispersion allows us to determine that the PLRs are significantly betterdescribed by a broken slope at ten days than a linear slope. The use of oursample as an anchor to determine the Hubble constant gives a $3.2\%$ largerHubble constant compared to the Riess et al. (2012) sample.

The M31 Near-Infrared Period-Luminosity Relation and its non-linearity for $\delta$ Cep Variables with $0.5 \leq \log(P) \leq 1.7$