The kinematical parameters of the local field RR Lyrae population and the zero point of the log P – < M _ { K } > relation for these variables are inferred by applying the statistical parallax ( maximum-likelihood ) technique to a sample of 182 RR Lyraes with known periods , radial-velocities , metallicities , K-band photometry , and absolute proper motions on the ICRS system .
Hipparcos , Tycho-2 , SPM , UCAC , NPM1 , and the Four-Million Star Catalog ( Volchkov et al . [ ] ) were used as the sources of proper motions ; the proper motions of the last two catalogs are reduced to the Hipparcos ( ICRS ) system ( Dambis & Rastorguev [ ] ) .
The K-band magnitudes were adopted from the list of Fernley et al . ( [ ] ) and supplemented by the data of the 2MASS Second Incremental Data Release .
The parameters of the velocity distribution are found to be ( U _ { 0 } = -10 \pm 10 , V _ { 0 } = -51 \pm 8 , W _ { 0 } = -14 \pm 
5 ) km/s , ( \sigma _ { U } = 62 \pm 10 , \sigma _ { V } = 45 \pm 8 , \sigma _ { W } = 28 \pm 6 ) km/s and ( U _ { 0 } = -23 \pm 13 , V _ { 0 } = -213 \pm 12 , W _ { 0 } = -5 \pm 8 ) km/s ( \sigma _ { U } = 157 \pm 12 , \sigma _ { V } = 98 \pm 8 , \sigma _ { W } = 91 \pm 7 ) km/s for the thick-disk ( 41 stars ) and halo ( 141 stars ) objects , respectively .
The zero point of the infrared PL relation of Jones et al . ( [ ] ) ( based on the results obtained using the Baade-Wesselink method ) is confirmed : we find < M _ { K } > = -2.33 \cdot log P _ { F } -0.82 \pm 0.12 compared to < M _ { K } > = -2.33 \cdot log P _ { F } -0.88 as inferred by Jones et al . ( [ ] ) .
A conversion of the resulting log P - < M _ { K } > relation to V -band luminosities yields the metallicity-luminosity relation < M _ { V } > = +1.04 + 0.14 \cdot [ Fe/H ] \pm 0.11.Our results imply a solar Galactocentric distance of R _ { 0 } = 7.6 \pm 0.4 kpc and an LMC distance modulus of DM _ { LMC } = 18.18 \pm 0.12 ( cluster RR Lyraes ) or DM _ { LMC } = 18.11 \pm 0.12 ( field RR Lyraes ) , thereby favoring the so-called short distance scale .