The kinematics of K and M dwarfs in the solar neighborhood are analyzed statistically using the sample of stars that were selected spectroscopically by Vyssotsky. We use all available information: photoelectric photometry, trigonometric parallax, proper motion, and radial velocity, in a global maximization. The procedure can rigorously handle errors of observation and incompleteness of the catalog over photometry and derive unbiased values of the kinematic parameters with reliable error estimates. The kinematical distribution of K5 to M5 dwarfs is represented as a sum of discrete components, each described by an anisotropic velocity ellipsoid and asymmetric drift. The maximum-likelihood model has typical young disk (σR, σφ, σz, va) = (31, 18, 12, 7) +/- 1 km s-1 and old disk (σR, σφ, σz, va) = (54, 36, 31, 23) +/- 3 km s-1 kinematic parameters and rms error estimates. The peculiar motion of the Sun relative to the LSR is estimated as (U☉, V☉, W☉) = (8, 7, 6) +/- 1 km s-1. The young disk dwarfs show a vertex deviation of 12° +/- 4°. The old disk K and M dwarfs are significantly less luminous than the young disk dwarfs of the same color, with a difference of 0.7 +/- 0.1 mag at (R - I) = 1.0 and which increases with redder color.