We propose a consistent (without any fitting parameters) statistical theory of classical noble-gas crystals with pair interaction between atoms. Using the equation for the single-particle distribution function of the statistical system, we demonstrate the existence of an infinite number of exact sum rules for the amplitudes of the space-periodic solutions. Even the first sum rule leads to the solution which turns into the exact one at the absolute zero temperature. For the pair distribution function, we obtained the physically correct solution using the well-known exact relation for the compressibility as the self-consistent condition. As a result, we succeeded in recovering the equation of state of the crystal, and starting from the Lennard-Jones potential with the "gaseous" parameters, we calculated the temperature dependencies of the lattice constant and the isothermal compressibility of the crystal at the sublimation line. These calculations (including the form of the sublimation line itself) agree rather well with the corresponding experimental data for the argon-type media in the "classical" temperature region. The question about the bifurcation of the solutions is considered. Ways to further develop the theory are discussed.