The M31 Near-Infrared Period-Luminosity Relation and its non-linearity
  for $\delta$ Cep Variables with $0.5 \leq \log(P) \leq 1.7$
  We present the largest M31 near-infrared (F110W (close to J band), F160W (H
band)) Cepheid sample so far. The sample consists of 371 Cepheids with
photometry obtained from the HST PHAT program. The sample of 319 fundamental
mode Cepheids, 16 first overtone Cepheids and 36 type II Cepheids, was
identified using the median absolute deviation (MAD) outlier rejection method
we develop here. This method does not rely on priors and allows us to obtain
this clean Cepheid sample without rejecting a large fraction of Cepheids. The
obtained Period-Luminosity relations (PLRs) have a very small dispersion, i.e.
0.155 mag in F160W, despite using random phased observations. This remarkably
small dispersion allows us to determine that the PLRs are significantly better
described by a broken slope at ten days than a linear slope. The use of our
sample as an anchor to determine the Hubble constant gives a $3.2\%$ larger
Hubble constant compared to the Riess et al. (2012) sample.
