RR Lyrae variables: visual and infrared luminosities, intrinsic colours,
  and kinematics
  We use UCAC4 proper motions and WISE W1-band apparent magnitudes
intensity-mean for almost 400 field RR Lyrae variables to determine the
parameters of the velocity distribution of Galactic RR Lyrae population and
constrain the zero points of the metallicity-<MV> relation and those of the
period-metallicity-<MKs>-band and period-metallicity-<MW1>-band luminosity
relations via statistical parallax. We find the mean velocities of the halo-
and thick-disc RR Lyrae populations in the solar neighbourhood to be (U0(Halo),
V0(Halo), W0(Halo)) = (-7 +/- 9, -214 +/- 10, -10 +/- 6) km/s and (U0(Disc),
V0(Disc), W0(Disc)) =(-13 +/- 7, -37 +/- 6, -17 +/- 4) km/s, respectively, and
the corresponding components of the velocity-dispersion ellipsoids, (sigma
VR(Halo), sigma Vphi(Halo), sigma Vtheta(Halo)) = (153 +/- 9, 101 +/- 6, 96 +/-
5) km/s and (sigma VR(Disc), sigma Vphi(Disc), sigma Vtheta(Disc)) = (46 +/- 7,
37 +/- 5, 27 +/- 4) km/s, respectively. The fraction of thick-disc stars is
estimated at 0.22 +/- 0.03. The corrected IR period-metallicity-luminosity
relations are <MKs> = -0.769 +0.088 [Fe/H]- 2.33 mathoprm log PF and <MW1> =
-0.825 + 0.088 [Fe/H] -2.33 mathoprm log PF, and the optical
metallicity-luminosity relation, [Fe/H]-<MV>, is <MV> = +1.094 + 0.232 [Fe/H],
with a standard error of +/- 0.089, implying an LMC distance modulus of 18.32
+/- 0.09, a solar Galactocentric distance of 7.73 +/- 0.36 kpc, and the M31 and
M33 distance moduli of DM(M31) = 24.24 +/- 0.09 (D = 705 +/- 30 kpc) and
DM(M33) = 24.36 +/- 0.09 (D = 745 +/- 31 kpc), respectively. Extragalactic
distances calibrated with our RR Lyrae star luminosity scale imply a Hubble
constant of ~80 km/s/Mpc. Our results suggest marginal prograde rotation for
the population of halo RR Lyraes in the Milky Way.
